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L'évolution de l'univers

Nguyên Tân Tài

Squaring Circle

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The determination of the natural constant Pi with the compass and straight edge.

After succeeding to square a circle and to do the reverse operation, it was prove that during these operations the different surfaces remain constant. A new method of different form surface comparisons was established.

The transformations of matter is a permanent construction of the universe. After these new knowledge of surface relationships, it is time to think on the fundamental natural constant value that sciences and technologies need for their developments. This text exposes the method of determination of a new precise natural constant value for Pi.

This long text is divided in two parts :

1) - 1st part is this text here,

2) - 2nd part is the continuation. Please Click herafter :

3) - 3rd part continuation. Please Click herafter :


A natural factor of form change

Changing forms?
It is the Absolute Space main characteristic
done according to the Matter Conservation principle.

Here is a new text describing such change type:
Its whole resolution by the Dakhiometry.

If you are the most closely concerned, please, click on this following link:

- determine the validity of the argument if x is irrational the square of x is irrational and pi is irrational (

- value of pi is irrational clarify the doubt with given some actual arguments (India)

The current Archimedes' Pi of Mathematics is Irrational. It is a fact in Mathematics. However, this irrationality has its root in the millenary mathematicians' erroneous thinking about Mathematics' nothingness objects.
From at least fiftenn years this site web was open. It see that not anybody knows that I am not a mathematicians. Really I am quite from the Dakhiometry discipline a rational science. It base of science rests on the Concrete discrete Absolute Space of the universe. While the Mathematics was built on human language words called as Numbers. Eveything in Dakhiometry can be described and constructed concretly with the spatial language in direct relation with any universe object. There is no Numbers in the universe but only the Quantity concept of the absolute space. There, no man's irrational believes is allowed. I had given in this web site so many actual reasons that point out this Mathematics big false conceptions with Numbers.
So, while staying on the spot I would like to go further for so much more true important problems that sciences yet ignore than, to have an unceasing chat with Mathematics self-absorbed behavior about their own quite particular irrational closed loop fantasy.

How can Rational may be compared with Irrational? How can reality can be placed aside the Nothingness? May it be some relationships between the Consciousness and the Unconsciousness? What does allows Aristote to cladified a Metaphysic aside in parallel to the Physics? Does it be originated from the universal laws or from man this eternal dualism obcession? Life is Science while irrational is from Ignorance even hidden under a Big Mathematics formulation.

In conclusion
Mathematicians ignore themselves that Mathematics is a most greatest man's Empirical Work, their first attempt of science. However they are missing the science gate entrance and science is now as a big fantasie growing world, the technology door.

- what is the meaning of PI in USA (, USA)

- large + "sacale" + of + institutional + changes + towards + equality + in + the + society (, Minnesota, USA)

- Determination + of + the + value + of + pi + theory (Ghana)

- bownload book the fundamental "spposes" of geometry (, Egypt)

- unique way of understanding the value of pi (USA)

- "discribe" + remedies + in + Viet+nam (VietNam)

- who + said + that + the + area + of + a + circle + is + pi + r + suared (, USA)

Probaby and surely, it is Me. One rcognizes there my own label or stamp or style and my fingers' claws.

- postulate one unique circle (, Netherlands)
- third axiom one unique circle (, Netherlands)

The just concept is really one unique cercle. The figure of a circle is no more than unique. There is an another unique figure according to its direct inheritance from a circle. It is the square. Starting from there, are born figures that are the successive forms, the basis for multiplicity constructions.

- GOLDEN + RATIO + animation .gif (, Politecnico di Milano, Italy)

The Golden Ratio is a factor for harmonious drawing proportion very used in artistic creation particularly applyed in works of Italian painters and then, in the whole world.
On a segment of line when a point is situated on its middle, this figure forms a central attraction of the view. Thus As one take this point as the main interest then all the rest of this figure will be secondary factors that are only to underline the central point.

While if a point is situated on this segment shifted aside in the golden ratio proportion of this segment then this figure means differently than as its unique centrifugation interest. This figure will be seen in its whole intrest of a point placed and belonging to its environment. There is no more one unique central point but a point relatively and dependent to the whole segment as its envirronment. This corresponds to a more usual situation for human global intuitive approach of the reality. Therefore the Golden Ratio on a figure appears as more harmonious for most of us.

However, the Golden Ratio on a line is only an analytical view point according to the linear mode. Harmony of figure is more complex. It is due to more wide manner that should be understood also with curlivilear mode. Therefore, we should see the Golden Ration also as in the area proportions and in the golden ratio of light contrast distrubution on a given painting aera and more larger in the whole 3D architecture system.

Originally, the Golden Ration is found in the whole figure of a pentagone. This is really a whole precise situation of sight that gives the Golden harmoneous effect. But one can found anywhere the linear Ratio as one can found anywhere the Anciant Pi measurements. In a complex and chaotic figure, it can be found by hazard a such golden ratio. However, its has no more the true magic harmoneous aesthetic effect signification. Despite these hazardeous golden ratios, to much chaos environment demolishes harmony. But a Golden Ratio between chaos aera and precise structures one, produces harmony. Such contrasting situations are used intuitively in modern painting and is no more linear methods.

The determination of a rational new and accurate Pi value.
by Nguyên Tân Tài

Law of Construction in Viêt-Nam

el universo y sus consecuencias; the universe and its consequences (, Venezuala)

What are Mathematics Impossibilities

- Please + explain + the + mathematics + behind + why + squaring + the + circle + and + trisecting + an + angle + problems + are + impossible + the + explanation + should + include + concepts + from + abstract + algebra. (, Miami, USA)

The argument for Impossibility in easolving some Mathematics problems was welknown by mathematiciens. I will try hereafter to give somme of my own reasons on the Algebra Impossibility.

Arithmetics and Algebra and also for the Analytic Geometry is that these methods rest on the basis of the Number invention. From there, as Numbers seems to be the Archetype of the universe, Mathematics try to describe anything in nature as being in space.

Note that Numbers can be basically represented with the Integer series. On any numerical base, we can represent Numbers as:

1, 2, 3,..., x,..., n.

However, it is really a simplistic archetype for the univers. Because, if we can go anywhere in the space, the Number-space is no more than this LINEAR system formed by Numbers from 0 to 9. In fact the 0,...,9 should be denoted as:

0, hole, 1, hole, 2, hole, 3 hole,..., hole, 9, hole

this is valid everywhere they are placed in a decimal order.

Transformation of thes successive Number/Hole, will generate obviously the Irrational Numbers as due to indetermined Holes.

Adding to this elemental Mathematics vocabularies, transformation of Numbers should use the Euclidean Division Algorithm where Hole transformation should reproduce themselves and give Holes.

Now with the whole Integer series, as written above, Mathematics believe that from any Numbers (x) Arithmetic and Algebra can use an equation to displace or link (x) to an another number, situated anywhere on this series. As being an universe archetype, it is the same thing that an equation is a Mathematics vessel that allows to go anywhere throughout the universe space.

Thus, the mathematic formalism as:
nth root of (x)
are not a Number or an Equation that can define its value.

For example,
nth root of (x)
can designates the whole Numbers series. This means that it is designating nothing.

Only according to the four operations as addition, substraction, mutiplication and division, can preciseley define a value.

All other formalisms for writting Numbers are only conventional conveniences of language symbols.

However, this is the basic difficulty and obstacle for the Mathematics using Numbers as tool as means for representing the universe even by abstraction. It is because from any given Number (x), there is no simple equation as for example from a given:


There is no possibility to go directly from the simple (x).

The reason is that going from one point (A) to the (B) one, it doesn't suffice to be a point characteristic. A Number (x)n can't give directly an (x) that is quite different to the [(x)n] position on anywhere of the Number series.

The Fermet Last theorem and the remarkable equation: (x)3 = a3 + b3 = ...
give us why it is an impossibility to get directly from any (x) position on the Number series, to go directly to any another Numbers of this series.

Concerning the Squaring a Circle and the Trisection of an Angle, there is two basic reasons that Arithmetic and Algebra meet Impossibility to resolve them. They are:

A) - Any Numbers are succession of language words in conjuction with a holes.
B) - Any Numbers series are not some universe Archetype because, in the universe space, anything can go from one point to an another location of the univers space. And the universe space is characterized by BOTH A DIRECTION AND A DISTANCE.
C) - It is why, because the Numbers series is a simplistic Linear structure without no reciprocal possibility of interchanging locations. A (x)n location can't be changed into an (x) one.

Therefore, the impossibility of the Trisection an Angle and the Doubling a Cubes, for Linear Mathematics is that in Numbers language:

The Third root of 2 is Impossible with Algebra method.

Why are the problems possible in the Dalhiometry method?
It is because using spatial language directly derived from the Space property, there is no hindrances as linearly going from point to point on a single line. But any problem can be resolved according to a more global view on space according to the Space Structure as synthesis of constructions. You may note the Squaring a Circle is there due to a complete permanent space Structure. It is also the case for the Trisection of an Angle, there is an unique space struture where the Trisection was fully expressed as the pure permanent Space property.

But why an x2 can be resolved? This is the case of the so-called Pythagoras property. However this latter was never explained rationally because the Pythagoras' relationship was only empirically discovered in practices.
The summation of two number squared can be resolved because it is the case allowed by a well known space struture given by a triangle rectangle inscribd in a circle. Precisely tell, it is the Dakhiometry Lam-ca structure. This is precisely possible owing to a space structure and not by any Algebra formalism. It is why Fermet that manipulated algebraic formalism, ignored that his Last theorem is false becaure a such relationship should rest on no else than on a specific space struture.

We can not imagine such global structure with dichotomic Number series. Because also in the Spatial language, the spatial structure also can represents the whole Universe Quantity structure. This structure can be applied on the continuity of any segment length as representing an unit of Quantity.

Therefore, any Number series is neither an Archetype of the universe nor something that can be used as basic tool for the universe knowledge because Numbers are too simplistic model, derived only from language words.

The rational conclusion is:
There are not Impossible problems for Arithmetics and Algebra but it is the Arithmetics and the Algebra as Number, that represent the impossible methods for resolving universal problem.

- Plato + saying + philosphy + is + the + contineous + study + and + struggle + of + life (Pakistan)

- Euclid's third axiom only one circle (Netherlands)

- using + a + compass + and + straightedge + is + it + possible + to + construc + rays + to + trisect + any + angle (

In fact, the circle remains still unknown. Really, the Geometry was formed on the belief that the universe heavenly bodies is floating in Nothingness. The Platoo copass is only a mechanical system that can produce a Practical-figure denoted as a circle or rather a wheel. The first intuition of Geometry was done from empirical observations.

The dividing any angle is from a natural spatial structure like the Squaring a Circle. That is the fact of a circle as completly formed by a CONTNUITY OF ANGLE SUCCESSION. As a Line is formed as a continuity of preseeding-and-succeeding Point, the perimeter of circle is rationally defined as a succeeding-and-preceeding Element-of-angle.
On a circle, any not-an-element-angle can be formed as an angle quantity that can be divided, particularly by Trisection division.
Therefore, with the spatial-language it can be spatially constructed this division and also by the whole 4-opertions.

This was proved in Dakhiometry fundamentally like was is done for the squaring a Circle. An angle is there defined as a given point of a circle that can "see" a same given Arc value on this circle. More generally, as Euclide's intuitively see it, there are really ONE CIRCLE in the universe. Therefore, an angle is an ABSOLUTE QUANTITY, independently to any figure form for example independenly to the Homothetie influence. Due to the Discretness of matter, any angle transformation is done also as rational determined quantity. Any angle transformation can be constructed with the Spatial Language.

The Dakhiometry Angle trisection is proved on any angle value in the continuity of a circle perimeter. The Squaring a Circle proved that Equality between circle an square indicate the Fulness of matter in the universe. As for the Minimal length that is reduced to the elemental matter point, it is also for an angle on a circle that is defined by Three-Elemental-Points of matter forming this circle. There is NO-ZERO quantity more generally tell, there is no absolute-VOID or Nothingness in the universe.

- mathematical + formula + used + by + g-tech + corp. + for + play + whe + games + in + Trinidad & Tobago (, Miami, USA)

- the + impotance + of + copyright + when + creating + computer + graphics (New Zealand)

- the impotance of mathematic in everyday life (, South Africa)

- Viêt + Nam + building + contruction + law + regulation (, Vietnam)

- mathematic + behind + the + proof + of + the + impossibility + of + squaring + the + circle (, Embarq Holdings Company LLC)

- the + immortal + birth + of + mathematics + circling + the + square (, Utimate Internet Access, Southern California, USA)

The mathematics behind the impossibility of squaring the circle is the just understanding of this proof event. It is the event of true and real space understanding from there human can get unbounded knowledge on the wealthy of universal life. A such knowledge is necessarily unlimited as the construction of universal laws are. It is how to access the human capacity of deductive though, a mode of universal laws construction according to aborscence process. This latter is like the sphere property of how to grow and extend from a center to build its peripherical surface not because a dependence of some center pressure but according to the surface enrichment resulting from arborescence process.

- what + to + do + to + accelerete + achievement + of + education + for + all (Tanzania)

Liberated from usual prejudices on each human capacity, everyone can then develop his own possibilities for contribution to the wealthy universal life knowledge.

- importance + of + circle + and + its + properties (Mauritius)

Actually. So great is the circle property consequences for our propensity of space investigation.

- pi + value + determination (Sheridan College Institute of Technology and Advanced Learning, Ontario, Canada)

- pythagore + international + pi (Governement of Newfoundland Labrador, Canada)

- why + squares + are + not + circles (, Florida Atlantic University, USA)

- where is the radius on a circle (USA)

I'm sorry. It should be: radius = Radius of a circle. I'm confusing it with the light rays shining from a Solar center.

- pi + accurate (The student Union of Helsinky University of Technology, Finland)

- quadrature + du + cercle (Wanadoo, France)


Because of some confusion in Search and Replace key, there is some extended not optimal world in this text. Please, the most easyest means for a temporarily equilibrium is to note this following world convention:
"area" = aera

- the + famous + Greek + mathematician + physicist + and + astronomer + who + shouted ++ eureka ++ when + he + discoverd + his + famous ++ principe (Canada Québec)

- mathematic + proof + in + life + with + real + analysis (Malaysia)

- calculation + of + pi + value + in + non + Euclidean + geometry (Italy)

- beyond + the + pride + free + download (Vietnam)

- forbiden knowledge (Croatia)

- squaring++the+circle+++ relationship ++ of + heaven + and + earth (USA)

These are human words. However its have a quite rational meaning. Because the suqring a circle is the key of mastering space knowledge. We human are not closed up on a planet even if the Earth is for us a most actractive cradle. It is why understanding the space matter through the Space Constant allows us to enter in the heaven to enlighten more justlty the celestial of heavenly bodie formation mechanic. It is from there our real origin of existence and thus understanding the whole universe space is a first basic step of understanding life.

- Uncertainty + in + "area" + of + circle + because + of + Pi + value (India)

- the + day + all + measurement + disappear + from + our + life + like + compass + scale + etc + related + to + maths (India)

... is the day where human becomes schizophenic.

- why + is + it + impossible + to + square + a + circle + and + what + does + this + have + to + do + with + pi (Canada)

You know it the origin of the impossible law coming from the last centuries where mathematicians became impotent in geometric resolution of some problem. The origin comes from the epoch where mathematic diverged into usual use of conventional language to measure space with the possibility to expresse space with numeric expressions. This a quite imprecise method and doesn't fit with the universe space element precision. Thus with the squaring a circle, the angle trisection and the doubling a cube, mathematicians telle that any number can fit with such problem resolutions. Thus is impossible what can't be constructed withe only the compass and the edge. And number that are used to measure such impossibility is somme irrationnal and transcendental ones. Here is the real repudiation of space by the human number language. The real orign of such gulf between space elements with the human number language worlds was from Pythagore that have a great devotion with his number inventions.

In fact theorem of impossibility means really theorem of mathematician Impotance to get the understanding the spacial elements with which they are directly built for life.

The Pi has nothing to do with the squaring a circle because it is a simple particular trick for the Anciants to try a definition of the circle perimeter with its diameter.

Only the squaring a circle can give the Space Constant with which a real vast gate is opened for allowing to enter in the matter space of the universe. A simple example is how it allows to know by deduction aeras and volumes of solid forms. The notion of the old Pi is far from such possibilities.

- accurate + experimental + value + of + pi (Pakistan)

Congratulation for such measurements. Because it need a high sensitive and precise measurement device, at least with accuracy of 1/1000 !

- precision+measurement +through +verification +of+ the+value +of+pi (India)

- pi cake infinite (Iceland)

- What is "mathamatic" pie (New Zealand)

- circle + mystery + mathematics (Colombia)


- new + value + for + pi (Iceland)

- when + was + "mathamatical" + pi + invented (Canada)

If a "mathamatical" Pi is concerned then, may be, it is the one described in this text as the Space Constant.

I resolve the squaring a circle during spring 1982. It took me about least than one week (exactely 3 days) to reach a convinced solution of the squaring by spatial figures. However, I need approximately two months to turn over and over around it to have a steady and clear valid solution. The reciprocal of the squaring a circle was discovered during this period. Then after that, I have to do bibliographic works to have a global view of what was done about the Pi and the squaring a circle all along its history. Note that because I did not have a clear idea on the anciant's works on the squaring a circle that I succeeded easily to resolve this problem. It is because I had no preconception and was standing before a virgin field where I had to create everything for thinking. I can't talk about and reveal my discover of the squaring solution to anybody. Everybody in scientific world are deaf as a post about a such problem and also I prefer to do not being bored stiff and then to be qualified as raving mad. Some more long years was needed to really understand and to construct the real basic proof of the Squaring a circle phenomenon in the universe. It consists to prove the equality of surface of two different figure forms. It is due to my knowledge on the basis of circle properties. The result in the present days, is to know many ways of how to construct a squaring a circle and a most important aspect is how to use and apply the different modes of the Space Constant to resolve multiple rational and precise space problems. The rich consequences of this Constant is truly endless. It is really the key of rational space knowledge, physically and mathamatically.

- Natural factor (India)

- what + is + "teh" + definition + of + pi (Canada)

Space appears in two different forms of continuity denoted as its recurrence property. There is a real Space Constant for space harmony to link these two different forms of continuity. circle and square mutually inscribed contain the relationship of these two different space continuities. It appears as a Constant allowing direct transformation between circular curves and straight line.
According to this Space Constant, complete forms transformations can be done in space for construction. Particularly, the surface and volume of different basic solid forms are easily precisely determined owing to this Space Constant. The Ancieant's approximate Pi is only a particular name of a composant of this Universal Space Constant linking the circle diameter and its circumference.

- how + do + you + determine + "teh" + value + of + pi (Bangladesh)

- how + invented + "th" + number + pi (UK)

Pie was produced by cooker before the term Pi come to any thinking. Thus, it was the proof of an anterior invention of "e" for a lunch before a good scientific research for Pi.

- proofs + explaining + the + importance + of + pi + because + of + its + role + in + a + circle + relationship (USA)

Actually. And more Pi is a key allowing to get the mastering of volumes and gravity center. And also is very important, how to get the space direction denoted as Angle. This is done through the Constant that allows a direct corresponding portion of curve to a segment. This is the authentic and exact trigonometrie.

- influence + of + squaring + the + circle + on + pi (UK)

- how + accurate + is + the + value + of + pi (, In2cable, India)

- MOST + ACCURATE + VALUE + OF + PI (Netherlands)

- pi + ying (Japan)

- proofs + of + the + value + of + pi (Brunei Darussalam)

- invented + mathematic + pie

- "proff" + resolution + simple + example (Sri Lanka)

- between + a + circle + and + a + square + equation (Monaco)

- formula de constante (Venezuela)

- pi + symbol + founder + applications + origin (Bhutan)

- Inventor + of + Pi + Day (USA)

- if + two + different + planes + intersect + their + intersection + is + what + "fugure"

- PROVE + THAT + A + SQUARE + IS + A + circle + proof

- The + rational + new + Pi + accurate + value + resolution

- what + is + now + the + greatest + value + of + PI ? (Hong Kong)

This is a fundamental question.
Since millenaries, there was a Pi value fluctuations. There was le lowest; then the greatest, then the longest Pi value. How can we play basketball when there are many balls on the playing field ? Fortunately, the Pi value is not particular human dependent. Now, it is simply a universe space constant. A such constant value is nor lowest nor greatest. Because of this universality everyone can accesses to this Pi value in reading the space. Therefore, we can tell that this universallity of knowledge is the greatest human gain.

- longest + pi + number + reached (USA)

Determination of Pi - if x is a rational number and y is an irrational number and z=x y is z a rational number or an irrational number? please give a brief explanation for your answer (, Atlanta, USA)

In the Dakhiometry it is proved that there is no irrational Number.
But, aside using a calculator, how are we used to do a multiplication?
This figure shows it. It begins to the first multiplication with the most right number of the lower part. Then when it is done, multiplication continues successively with its next left one until all the whole lower part digits is exhausted. Their results should be precisely ordered in columns to be added as a whole.
How can we do it if an irrational number, e.g. (3.1416...), is composed by ending points as "Not a Number" things? How can we ordered in columns a series of points where there is no possible distinction between points as a number can do it?

Any operation needs a precise determined quantity. A rational number is precisely characterized by a precise quantity. The precision property is both a Begining together with an End. Note that according to this definition, a Circle is a rational form.
An irrational number if there, is never ended. It means that it is never a precise quantity number.
Therefore, rationally done, any irrational number is a ghost and then can never produce any transformation into a (z).

- Petit + test + de + math +(+ s.v.p.:+ ne + paniquez + pas+)+!
+ Ceci + est + une + illusion + d'optique+.... avec + des + chiffres +! + Cette + énigme + doit + être + résolue + dans + votre + tête + sans + papier + ni + crayon.

++ Prenez + 1000 + et + additionnez + 40. +...
+ Afficher + davantage ++ Maintenant + additionnez + encore + 1000.
++ Maintenant + additionnez + 30. + Encore + 1000.
++ Maintenant + additionnez + 20.
++ Maintenant + additionnez + encore + 1000.
++ Maintenant + additionnez + 10.
++ Quel + est + le + total ++ Avez-vous + obtenu + 5000 ?

Determination Method of squaring a circle

At the time where this text on Pi resolution was presented here as it is, many basic theorems were not able to presented. Therefore, the basic proof of the surface equality can't be shown presently. Because there is an another spatial simple proof of surface equality between a circle and a square that needs a quite different basic spatial knowledge other than the classical Geometric methods. This are direct comparisons of different surface forms and not as a product of two sides of figures. Then you may note that this following Pi is a real rational precise constant of the universe surface property. This proff will be given a next day, when the basic Dakhiometry method will be exposed. There is now a new real method of spatial knowledge that the Geometry had known only with a very remote view.

The squaring a circle is a structured surface transformations. The circle an the square are different class of surface forms. However, if this change is a rational reality, this means that they are closely linked in a same matter structure. Because this latter is permanent it should remain somewhere in the circle and the square. This is the logic of matter memory.

Therefore, one should find this logic structure in space locations that are common for these figures, after their transformation. This is the reasons to paid attention at the intersection points of the circle and the square of same surfaces.

In this text are used mathematics symbols convention :

[ 1/2 ] = { 1/2 ], a half
{ . ] >>> multiplication
{ / ] >>> division
[ sqr(...) ] >>> Square Root of the expression in parenthesis.

Determination of Pi

Here on the left of this figure, are the circle and the square after a surface form change.

1 - Paid attention to the intersection points. They are placed around the circle and the square, with particular precise symmetry.

2 - With relations between these points, one should compute the red triangle, on the left. There is more of this triangle deduced from the central symmetry of the whole figure. This triangle will be expressed as functions of the lengths c, a and b of the triangle, draw on the right of the figure.

- Figure+1 + show + the + triangle + circle + square (Japan)
Thank you for this very interesting remark because it gives me an opportunity to throw light on the fundamental of thinking or reasonning.
It is probable that one can show a squaring a circle can be done by a triangle or other forms construction. Current Anciant mathematics' method is to use any geometrical object to build a solution. It is so when men want to build their houses, they take rock, sand, mud and vegetation, all what they can find around them. Next, one tells that he had created an object. This is the creation concept for human. Extending this concept one tells that there is a greatest being who can Create without the need of finding materials...
We can note that in this situation there is nothing really founded as a creation concept. This is only mechanisms of putting empirical ideas one next to the others and then from this heap of ideas man is going to descirbe describe the World. One can call this proceeding as an anthropomorphic imaaginary.

- prooving + pi (Isreal)

- "descirbe" + pi + determined (Australia) Spposed that for example, a triangle can make a square from a circle. From this result, there is no new idea, no new concept that can be revealed from space. In this case the fundamental question is : where does come from a triangle ? What is the postulate for a triangle and the consequences of this postulate ? Then somebody can invalidate this squaring a circle through the triangle, by proving prooving that the triangle need angle definition. Because angle definition is only precisely defined by the perpendicularity in a right angle. And where come from a right triangle ? Also there, a right angle is one property of the circle ! And where come from a circle ? Here our thought meets a logic crossroads and a circle is a direct Space Postulate : the circle is not a form. The circle is precisely the PERMANENCE REMNANT.

Therefore, as a square has precisely this right angle property then, a triangle that creates a square, is a TAUTOLOGY. Consequently, a triangle that allows to create a square from a circle is an illusion of anthropomorphic thinking type.

Now, why does on the figure-1 one can see a triangle in a circle ? The basic conscience is to see there only the consequence of an ALREADY RESOLVED squaring a circle. Because we got the square directely from the circle then, we can examine this finished construction for the purpose of measurement analysis. It is the real case from that we can get the next formula of the Space Constant.

You may note,
that I suggest to any mathematician interested on the question, the possibility of acquiring my works on the basic Dakhiometry theorems. Amongs theses theorems there are basic circle angular properties defined by theorems. Please, read the note at the beginning of this page.
Because I don't make repetitive long discourses on the consciousness of differences. I will end any more explaination nor newer proove other matter properties. I note that there is a real wall between the Dakhiometry and the current learning that underistimate or believe that the Dakhiometry is an obvious simple thing.

The figure-1 show the general process of the constant Pi determination. Then from the figure-1 we have relations following :

L22 + L32 = L12

a2 + b2 = c2

We are going now to compute the length [ Li ] with the a, b and C lengths.

Let us return back to the Beginning of the universe ! This is not a pompously speaking. The beginning of the universe is a rational Change of matter, why do we not included it in the rational talk? Remind that the Beginning of the universe construction is the squaring a circle. It consist first of inscribing a little circle in a quadrant of the great circle.

- geometrical representation of pi (India)

- astronomical intersection (, India)

- moment of inertia two intersection disks (Racunarski centar Univerziteta u Beogradu, Belgrade University Computing Center, Yugoslavia)

- geometric representation of proportion system (, USA)

- pi and geometric figures (, Romania)

If the new Pi is used in curent technologic application then there is a method of spatial caluclation that allows to get any length Pi applied in spatial construction of transformations. This allows do avoid the Algebraic systematic errors du to the bad division algorithm and to the irrational holes in Numbers theory. The spatial construction is very simple in calculation for example used by digital systems.

- fullmetal (, Japan, 6a3BnFoe/1191010050/namechanger.png)

- stone transmutation circle (Philippines,

- philosopher stone circle (Brazil)

A true stone when one have some unbounded sight of its lighting in the space structure understanding. But the true Space Constant is not in the form of the Anciant's Pi relatively to the circle diameter. The Space Constant is active mainly in the form of the ratio (Pi/4). The ratio forms is valid data for both linear and circular space aspects.

- full metal Alchemist transmutation circle (, Brisbane, Australia)

Really indeed. From lead into immutable golden Gold.

- pure geometrical constructions with ruler and compass (India)

I am sorry but anyone should remain in great contradiction when he persists to denoted the Dakhiometry as Geometry. This shows that he is misunderstanding the Dakhiometry new method and continues with a blindfold living in the narvel of a old dead Geometric empirical science. If one doesn't change his language vocabulary it is useless to seek some renew and he is degrading the Dakhiometry when seeing it as belonging to Mathematics set of tricks and recipes.

- the true philospher's stone (, USA)

It is really a true logic philosopher stone according to that it is used quite in magic manner, for planar aeras and volumes déterminations as a logic transformer agent.

- Full metal alchemist-alchemy circles (, Australia)

- Alchemy ancient philosopher stone (, Canada)

- how many straight lines can you draw in a circle (New York, USA)

If only lines of different Direction is in account then, there is unbounded number of possible lines.
It is as a given defined angle (A1) is written as:
(Bi) = (A1) + n.Pi
where n is any number to define unbounded direction (Bi).

- Fullmetal Inverse transmutation circle (, Canada)

- immortality circle trasmutation (, USA=

Its meaning is really the immortality of the universe construction.

- transmutation circle for a philosipher stone (, Florida, USA)

Actually. It can be The Circle as the Transmuttation event that creates the Philosophal Stone under the structure of Circle-Square.
Because a such Stone allows really, a so whealthy unbounded understanding on the universe constructions. This is the Golden unbounded Knowledge Transform series that opens a large precise horizon of conscience on the universe.
You are informed that amongst others, the Trisection-of-Any-Angle solution is given so simply from this philosophal Stone. The circle can be natuarlly divided by 2. the Dakhiometry can divide the circle by 3. This means that The Dakhiometry can divide the whole circle POINT-to-POINT.
The Circle properties are really the remanence of the universe principles ones.

- angle + trisection + 2011 + default + method (Egypt)

With the Diakhiometry Squaring a circle, it can be seen that most of mathematicians visitor of this site have a very little understanding of what is the meanning of a such problem resolution.
Most of them are eternally crying after their "Holly Pi". They are worshiping their "Archimdes' Pi". This shows that practical nobody have some just idea on a such important resolution.

The knowledge is a rational open way for accessing the universe realities. According to that science should rest on the man capacity of thinking using successive reasons, this means that science should rest on basic Facts of the universe. The squaring a circle is the determination of one main basic universe Facts. However, usual mode of mathematicians' thinking is to be formated by millenary dogma.
What can produce fogma?
It can be seen that Mathematics dogma produce only an amount of Tricks and receipts. The Pi is one of these Big recipes. Thus, with the squaring a circle most of mathematicians and scientists see the squaring a circle nothing else than a new recipe of "an Old Pi to adjust or to corrected". Thus, for most of the visitors, "from a Mountain was born a Mouse".
This a political or conservtism mode of society behavior but not a rational science method.

What have to do the squaring a circle and the Trisection of an angle? From the squaring a circle Fact, all the possibilities of chaining multiple ways of reasoning is like the sudden appearance of all the river sources on the Earth for science reasonning methods.
Understanding the squaring a circle, allows to get the understanding the space direction properties particularly what is denoted as the ANGLE.
Do one nows how Mathematics ave the understanding of an Angle?

Due to tle millenary dogma, Mathematicians has a false understanding on what is an angle. Mathematician temps to resolve the Trisection according to their ignorance on the Circular space. They see an angle with no more than a Linear Trick. One tempts to resolve the Trisection on the Linear figure of an angle formed by TWO INTERSECTING LINES. This is their famous lesson from Archimedes' trying to suggest a Trisection of angle on the riddle of two lines intersecting figure! Therefore what can we do when we talk about the Circular property while we are no more thing to do than with our big ignorance of the Circular property?

Now I tell what the squaring a circle allows us to built a New true human science that is not still existing from the beginning of the universe!

1) - The Squaring a circle allows the unify our knowledge on the Reality of the universe homogeneous and isotropic Space as the Simultanneity of Circular and Linear one.
2) - A straight length is quite different from a Circular one according to that Circular and Linear properties are Quite independent.
3) - An angle is not formed by two intersecting lines. This a millenary belief of the Ancients, the Gods of the Modern Mathematicians.
4) - The squaring a circle allow to see that The Time is an illusion of the another believes of the Anciant Gods. Anything of the universe should be understood by a True science as the property of the universe Space. The Trisection can be resolved simply with such New true knowledge.
5) - The squaring a circle seen as a trick to determine the old recipe Pi, is no more than the different societies that behave in their political and conservatism bahavior. This is a diagnostic of their civilisation being in decadent. Only rational and exact new science can allow wealthy Life developments in sociiety for human.

- endless giometric figures (Armenia)

- art + geometric + net (, Michigan, USA)

- transmutation + circle + physics (, Thailand)

Actually a transmutation physical event.
The circle (C1) is really the Golden Key to human Knowledge Golden Gate.

- step + how + to + use + geometric + construction (Philippines)

- full + metal + alchemist + human + transmutation + circle + explanation (Canada)

- "Tha" + universe + evolution (USA)

- Pi + and + Art (, USA)

- human + transmutation + circle (, Maryland, USA)

- easy + transmutation + circle (, Guam, USA)

- human + transmutation + circle + .gif (Philippines)

Further away the different institution conservatisms, when whith the true knowledge on Circle, well beyond the old one from mechanical compass made of, human transmutaion will be effective at an open gate for being wholy inscribed as an entire part of the whole universe reality.
However, the Circle is still non-existant in the current sciences.

- Philosopher's + Stone + Transmutation + Circle (

It consists to discover the Just-Stone and simply to put it at the Just-Place... - Philosopher's + Stone + Transmutation + Circle (

This really the case for circle (C1) the inscribed in a circle-quarter.

- Philosopher's + Stone + Transmutation + Circle (

- philosopher's + stone + transmutation + circle (, Annecy)

- Philosopher's + Stone + Transmutation + Circle (..)

- Philosopher's + Stone + Transmutation + Circle (

- stone + circles + Lebanon (, California)

- geometrik C5%9Fekillerle simetrik resimler (Turkey)

- Real + Blood + Demon + Transmutation + Circles (

- true + transmutation + circle (, S California)

Actually, the mutual Circle/Square transformations are from real transformations by Transmutation. A trasmutation is done necessary according to the Energy Conservation principle from pre-existent and permanent universe.

- Philosopher +Stone+Transmutation+Circle (, Texas)

It is really one amongst many rational tools used by matter for transformation.

- Blood + Transmutation + Circle

Determination of Pi

The symmetric positions of the two great circles show any relationships that allows to place the same little circle C1 in the different precise locations of the figure. Particularly we can note that :

L2 = R of C1

- construcciones + geométricas (Mexico)

- Transmutation + Circle + Philosopher + S + Stone (

- how + to + draw + transmutation + circle (UK)

- number pi and arts (Romania)

- circle axioms (Bahrain)


- geometric constructions using straight lines, angles and circles (, Belize)

- draw transmutation circle (, Michigan, USA)

- philosopher's stone transmutation (Singapore,

This is the true notation for a such space-Key that allow the unlimited understanding of the universe space. This latter is the human intrinsic property that allows to get the real living for everybody. The basic understanding of the universe Facts is to have a good understanding on the whole space. This latter is no more than the true being language of life for the multiplicity.
Until now Mathematics methods are quite ignoring what is Space because they ignore that human knowledge needs a Key playing the role of a true philosopher-stone. This latter is no more than a necessary Key to open the knowledge gate.
It is why mathematicians can't resolve the basic three mathematic problems of the squaring-a-circle, the trisection-of-an-angle and the duplication-a-cube. Because we have to know what are the common "impossibility" points between these three problems.
Precisely, these three mathematic impossibilities is due to the ignorance of the space knowledge transmutation owing to a real "philosopher's stone".
These three mathematicians' impossibilities are due to the ignorance of the CURVILINEAR SPACE property!
On may note that the Dakhiometry can precisely resolve these above three basic problems -and more- because it is perfectly defined there the space as having the LINEAR and CURVILINEAR main properties.

Really the universe knowledge must be done fully throughout the direct and reciprocal trips between the Linear and the Curvilinear of the absolute space. The relationship between these reciprocal space need a Key for space transmutations that acts magically like this so called "Philosopher's Stone". The magic in no ùore than the direct space property application.

Practical Example:
All the object surfaces and volumes are preciely and simply spatially defined according the direct use of the Spatial Curvilinear Key. This latter is denoted in Dakhi-Hoc as the Space Constant TT. Consequently their mass-center can be also perfectly and rationally defined.

A such simplicity give the true notion of the reality denoted as the "Philosopher's Stone"!

Thus, we get a first determination of the length L2 :

L2 = R of C1

Now, what about L1 and L2 ?

The figure-3 is going to light it.

- what signe and symblos we can see in cubism (, New South Wales, Australia)

- mathematical formulation of cubism (UK)

- mathmatic (Korea)

- new + cubist + architecture (HongKong) - mathmatic (Taiwan)

- new Taiwan architecture (Taiwan)

- jardin + imaginaire + centre + de + symetrie (UK)

- fantastic + building + architecture + in + Taiwan (Peru)

- middle + school + cubism (USA)

- cubist + building + in + Saudi + Arabia (Saudi Arabia)

- Egypt + cubism (Philippines)

- Taiwan + fantasy + digital + art + fantastic (Bulgaria)

- cubist + architecture (Mexico)

Actually, you are right. Because the Dakhiometry knowledge use the universe absolute space language, it is really the Architectural Art for exact Science using true equality relationships.

- usuel + is + beautiful (Bulgaria)

May be, according to its authenticity.

- cubism + in + architecture (Vietnam)

- the + art + of + pi (Ireland)

- who + and + how + discovered + the + value + of + pi (United Arab Emirates)

Mystery of Human's adventure on Earth.
Pi is not a characteristic of the circle. Thus going towards the unknown Circle is like to catcjh at shadows.

But Pi is only the Linear factor in space. Fundementally, Pi is the Relationship the purpose of which is to get access into the basic Circular universe. It is why one should perform the Squaring a Circle to get the Pi revealed, this relationship: the handshake-Pi between the Circle and the Linear Square to be abble to get the unbounded matter relationships enlighten in universe Space.

- pi + get + real + geometrik (Greece)

Determination of Pi

1 - In this figure, we can see that L1 is equate to the half of a diagonal of a square of an edge of length C

It appears to me that there was some objections about the proof of the Lenght [L1].

It seem to me because there is no clarifyed objection and I do not understand what it concerns from some unprecise words.

And may be, there is some pleasure to say
- erroneous + demonstration...

Well with such "mathematical rigors" I understand how mathematics stand momified since a so long thousand years.

Then, hereafter are resumed how [L1] is equated.

Note for someones that he can not prove that there are somme mathematical errors in my proves. This is because I can prove them in different ways that yield sames results.

Now, to show that I have proved the equality of lenght [L1] let us resume the anterior figure of an anterior text where it is shown how [L1] is equal to the half of the diaginal diagonal of the square of side |c].

- circle + theorems + 7 + rules (Russian federation)

- sancal + Singapore (Singapore)

- line + square + circle + triangel + architect (Norway)

- six + circles + theorem (USA)

- matematic + sqaure (Myanmar)

- matematic + logo (Mongolia)

- mathematical + impossibility + formula (Finland) - cubism + architecture + mountain (Iraq)

- architect + calculation (Australia)

Information may be precisely get from arcitectural structure.

- eureka + Kuwait + vector + logo (kuwait)

- teoremler geometri (Turkey)

- pi + get + real + geometrik (Greece)

- the - physical - impossibility - of - garfield - in - the - mind - of - someone - living (, Oregon)

- Squaring + the + Circle + Proof (

Détermination de Pi

- cubist + architecture (Singapore)

- diagonal + of + the + square + proof (Poland)

- cool + things + in + Germany (, USA)

It is there remarkable that a square inscribed in a given circle is also point-to-point inscribed in the corresponding transformed square of this circle. This means that the common inscribed square aera proves that the circle and its transformed square aeras are both equal.
Therefore, the triangle (L1-L2-L3) aera is equal to the one of the circle sector of chord (L1).

- square + and + compass + Ireland (Ireland)

- square root compass ruler (Germany)

- cool things to do with a compass and straightedge (, s.o. Calofornia, USA)

- how to draft a golden rectangle with a compass and straightedge (, Massachusetts Rhode Ismand School of Design, USA)

- mathmatic (Mongolia)

- the construction of the mathmatic golden compass (, Israel)

- tangent and normal lines in circle (Malaysia, courses/m309-01a/montero/page28.jpg)

- vicious circle ekonomi (Indonesia,

- The Cosmological Circle (, USA)

Really, the circle is the circular cosmos remanance appearing everywhere in the universe construction. It is why looking reality through the circular structure can reveal solutions of most problems.

- Pisagor teoremi (Turkey)

- NZ inventions (, New Zealand)

- Cosmological Squared Circle Pics (, New Zealand)

- technicaldrawing Underground New York (TU-Berlin.DE, Technische Universität Berlin, Germany)

- parabol circle equal radius (Vietnam)


- history + Pithagoras

- square inscribed in circle (USA, New York State, Syracuse University)

- inscribed a square in a circle (Dublin City University, Ireland)

- pi equals (, Maryland, USA)

On this figure it was tell that an extended Pythagoras' theorem is used.

For circles
|A] + [B] = [C]

For squares inscribed in this circles :
square[A] + square[B] = square[C]

These relations are deduced from analysis of the squaring the circle.
The conclusion is that [L1] is the side of the square inscribed in the circle [C] .

Now, with a simple new effort, you may double this square of side [L1]. Thus, you get the square of side [c] that is the square circumscribed of the cercle [C]. Consequently,

[L1] is actually the half diagonal of the square of side [c] as it is said above.

These are sufficient mathematical reasons of the proof of the [L1] equality. No need to turn around other strange tricks.

Note also on the figure :
According to the symmetry of circle (C) and its transformed square one get a direct relationship :

b = L3 - L2

Therfore the [b] value is given in the formula listing as next below.

I verify it, there is no thoughtless errors in writing this HTML page, at least for what is concerning here on the Pi formula. - rond + square + number

2 - And for L3, we have (a + b)/2

From figure-3 we can see the length value of L1 :

L1 = (1/2).(c).(sqr(2))

Note that [sqr(...)] means Square Root of the number in the following parenthesis.

On fig-3, it is clear that the sum of the C2 and C1 diameter is equate to the edge length of the square that is the length [ a ]. With the placement of C2 and C1 on the square edge, it is obvious that :

L3 = (1/2).(a + b)

We have succeed to evaluate the red triangle of figure-1, as function of lengths a, b and c. Resume it as follows :

L1 = (1/2).(c).(sqr(2))

L2 = R of C1

L3 = (1/2).(a + b)

The job is not quite finished. Because L2 is function of an unknown radius of C1. Let us go for determining the radius of the circle C1 with the following figure-4.

Determination of Pi

The diagonal of a square circumscribed to circle C has a known difference [d] with its edge. This is the diameter [d] of the circle C'1.

Now considering a homothetic of center O, we can concluded that the circle C' is equate of 2.C. The result is that :

C'1 = C1

- Square + root + proportion + in + architecture (Egypt)

- pi circle (Argentina)

- equivalent square width of circle (,, State of Missouri, USA)

- polygon circle constant (Korea)

Golden circle C1 with the Dakhiometry Calculator Structure

- how to structure a transmutation circle (, Michigan, USA)

You underline there the efficient basic space method.
The usual mathematic problem is to pose any factor on a problem then, to turn around this latter to find some remarkable points that may give a solution. This is a true empirical randow manner.
However, knowing that any problem is necessary inscribed in the space, therefore, any problem should be from a spatial structure. It is because without such basic spatial law, there is no universe reality but only illusion.
Thus, the true solution of any problem is to find at first its space environment. because any of it solution is necessary inscribed there. With a better acquaintance of the space properties, we can rapidly place a problem in a space structure. It is the real way for a method that drives to the solution, with a real certainty on it.
This should be the only rational way for any science.

- application + of + circle + squaring + to + determination + of + pi (USA)

Because the relationship between a Curve and a Line is a Great problem, its resolution is directly get from the Squaring a Circle construction. The relationship between a Curve and a Line is precisely there and no elsewhere.
It basic proof is that the Space is not Manipulation of Forms but is strictly constructions with elements as Points, Lines and Curves.

- beauty - pictures - relating - to - direct - and - inverse - variation - in - the - field - of - mathmatics (, Japan)

- Hô + chí + Minh + vector (Vietnam)

"Minh vector" is significant to "enlightenment vector"

- visual structure of plane using square triangle circle (Pakistan)

This squaring circle construction and calculation, proved really that universal law are expressing only in planar 2-dimensions mode.

- geometrical + determination + of + pi (Argentina)

- geometric + constructions (Philippines)

This Space-calcultator is an authentic spatial-structure creation to get the solution.
One can note that all the Squaring a Circle method, are done successfully according and certainly only to the Dakhiometry method of space-structure creations!
It is the real Dakhiometry method that has nothing to do with the current Mathematics.

- construct + golden + circle (Austria)

- square quadrant circle top view (Netherlands)

It can be done the same central symmetry rotation for the corresponding circle (C) with (K). This shows interesringly their characteristic on corresponding intersection points. These latter define the position of the triangle (L1, L2 and L3) in this structure. These common intersction points, are situated by the central square with (E, O and F) as diagonal.
This structure proves that the circle (C1) is precisely inscribed in a quarter of the circle (C) with its radius dimension.

- The + Golden + CIRCLE + TRIANGLE (Saudi Arabia)

The Golden Fleece for answering to the Sphinx' enigma...

- finding pi exact value indestructible clothes (Australia)

- pi + formula (Croatia Hrvatska)

- math formulas for pi (

- math + nature + formula + pi (USA)

It is justly tell.
Universal laws have only to read themselves to construct. It is noted that human should also read the self to know the universe.

- A + measurement + that + is + accurate + is + one + that + a. is + as + exact + as + possible + b. is + close + to + the + true + value ++ c. contains + at + least + four + significant + figures + d.contains + five + decimal + places (, USA)

- prove + pi + value (Thailand)

- alchemy + circle + with + meaning (, USA)

- symmetric + property + of + equality (, (Los Angeles Unified School District, Califormia, USA)

Actually, symmetry has the property of equality. It can be used with fertility if one can have a global view to determine the structure and localizes there the just corresponding center of symmetry.
This means that one have to invents the problem in its space structure.

- compass + straightedge (, Washington, USA)

As you notice it, all the work are done with compass-straightedge concept.

- classic + method + calc + pi (Brazil)

- how + to + make + your + own + alchemy + circle (,USA)

- square + and + cirles + proofs (, Colorado Denver, USA)

- mathematics + "impotant" + resolution (Lebanon)

- prove value pi (Pakistan)

- determination + of + pie (Mauritius)

- the most exact value of pi (Poland)

- determination of the value of pi (Ghana)

- SYMMETRIC + PROPERTY + REAL + WORLD (s.o. California, USA)

The first access on Real world is done through the Space.
Basis property of space is symmetry. It is due to that basis of the univese is to be in circular Permanence. Therefore, necessary what is Real exists in Symmetry. Even if a rock generally appears with no-symmetry, however it is constituted with symmetric atoms and belongs itself to symmetric heavenly structure.

- theorem + of + continuity (stny, USA)

There are two independent aspects of the universe Space. It is the Curvilinear and the Linear space. However it is not representing a dichotomy in space. This latter appears in continuity as a whole homogeneous and isotropic Space.

- what + is + the + meanning + of + dertermined (, Ontario, Canada)

- the + doubt + of + accuracy (Japan)

- constant doubt leads to certainty (UK)


- pi + accuracy + for + whole + universe (, USA)

- construction + measurement + Circles (, California, USA)

The circular defined, it gives means for true basic measurements. Particularly, a circle is also a LENGTH, THE CONSTANT LENTH.

This means that the circle give to us the Constancy for defining the different between speed of movement. It is to tell, there is no TIME, the millenary belif illusion of man.
Note that difference of movement is expressed as the Speed or velocity (Length/Time). This is no more than a conventional based speed stated on the conventional unreal Time. A, universal constant Length, allows to rationally express the movement characteristic that we know as speed.

From now, it can be rational express the different movements as:
[ (any-Length-of-dispacement) / (Universal-Constant-Length-Unit) ]

The circle furnishes to us THIS UNIVERSAL CONSTANT LENGTH.

This rationally proves that TIME is an another man's illusion.

- mathematical + constantas (Georgia)

It is a most fundamental constant, that should be use for replacing the artifiical Time. Time is a millenary illusion for man. Time is introduced because man had a bed understanding of the Movement phenomenon. I will expose the Why and the How Movement is a whole pure spatial phenomenon

- PI + VALUE + NEWER (, Greece)

- center + of + circle + mass + calculator (Latvia)

- calculator + structure (Cambodia)

- mathimatical oprators order (Pakistan)

This is the most exact concept definition for this new spatial method. In Dakhiometry, there is a complete spatial mode for calculation using spatial elements for exact determination of spatial structure quantities. The whole 4 operations are easily used for figure calculation. The Dakhiometry is not belonging to Mathematics that are no more than a heap of huge complicated Tricks and Receipes using Numbers Literatures. On must be in conscience on the retardation of this empirical Mathematics. Quantity ans Space is ignored in Mathematics even if these "words" is in everyday use. It is the main condition to be abble to build a human True Modern Science.

The fact is that most of visitors are always crying to their famous "Archimedes' Pi" proves that practical everybody hasn't some understanding on what it is exposed here!

This above construction for calculating the Pi value from the spatial strucure, is a one that I had used for a more best understanding with mathematicians and their usual methods and their eternal and mystic pythagorean theorem.

However the Dakhiomatry methods are more general than the usuel Mathematics tricks and receipes. The true initial Dakhiometry calculations are done directly from the method denoted as the Dakhiometry Calculator Structure. Here next is shown an example of its application to clarify a given problem analysis.
However, this new true concept is difficult to be understood. We are used with Time from along all millenaries and also the circle is not yet well know by most of mathematicians, particular by everybody on Earth!

- From + Cubist + Architecture + to + Modern + Simplicity (Jordan)

- overcome inaccuracy of arcs using pi in code (UK)

- pi resolution (, Philadelphia, USA)

- draw + a + geometric + circle + box (Pakistan)

- exact rational value of pi ( Washington, USA)

- NUMBER + PI + ART (Greece)

If it concerns this mode of finding the numeral of Pi the, it is also an Art.
It can be noted that a painter creating his paint, is also acting with a science. The science of how to know that what he is telling is also the coherent with the feeling of any other observer. The science of how to tell exactly what he assumes that he had the sensation of an universal reality. If looking at a paint we get an esthetic feeling, it is because we are recognizing that something in this paint is the universal true. Therefore, a painter is practizing the Art of feeling a certainty with his Science of concretly constructing and describing this reality.

- circle + proximity + to + square + architecture (, Virginia, USA)

- simbol + giometrik (Indonesia)

- architecture + circle + structure (Cambodia)

- square + circumscribed + about + a + circle (

- squaring + the + circle (MSUS.EDU, USA)

- portuguese + cubism + paintings

- new + value + of + pi(Kowait)

- formula + cubisme (Malaysia)

- value of pie remains constant (India)

- value of pi remains constant for any circle (India)

It is not because of the correspondence between the circle and its perimeter as for the Anciants belief. An internal constancy is only a particular property of a figure. For example, a side of a square is constant with its diagonal, is only a particular constancy.
The constancy need to be a function between two independent figures. In this case, this means a fundamental relatinship in space.
According to this axiom and to the constacy length as the result of the squaring a circle, this contancy is the relatinship between TWO BASIC FORMS, the circle and the square. Therefore, it is the presence of a universal space FACT that can define really main basic of these consequences for the space knowledge. The Dakhiometry yet had unfolded some of this most basic consequences.

- squaring + the + circle (Denmark)

- the + diffrence + between + the + circumfrence + and + the + diameter + of + a + circle + is + 30 + cm. + Fimd + the + area + of + the + circle (

Help... ?

- history + of + Mathmatic (Iraq)

- pi + in + maths (Turkey)

- cubist + architecture (Australia)

Actually. The spatial language is the true architectural one of the universe.

- architectural language circles (Texas, USA)

- cubism + in + architecture (Egypt)

- how + to + calculate + area + inside + a + square (UK)

Actually. It is the basic purpose of the squaring a circle and is not only for simple internal relationships of a circle. But not only for the fundamental circle but it is a key for wealthy consequences in the understanding of the whole space Forms.

- rational + values + of + pi (, Venezuela)

- golden + circle + and + architecture (,uk, UK)

- what is chili pie and value maths (

- architecture + along + a + circle (Austria)

- third postulate one unique circle (Netherlands)

- importance of pi in maths (India)

- what is it called when you use a compass and straightedge to construct a square exactly equal in area to given circle wich society brought us the first known reference to pi in history (, Indiana, USA)

- most + inaccurate + value + of + pi

- what + is + pi (, USA)

- squaring + the + circle + proofing (, Fiji)

- squaring + a + circle (UK)

- define + postulate (, UK)

At the beginning, was the central symmetry...

- pi + formula + in + architecture (, USA)

Pi is effectively the result of an architectural arrangement in space.

- cricle + k + Japan (Indonesia)

- prove that circle cant get into a square (Cyprus)

- sumatori + pi + formula

- parabol + calculator (Mongolia)

- construction of a golden circle (Kuwait)

- new mexicans for science and reason (, Indiana, USA)

- which value of pi is doubted for circle diameter ratio for unification theory (, Athens, Greece)

- quadrature + of + the + circle (, Belgium)

- Euclid's third axiom: unique circle (, Netherlands)

Consequently, the Square is the Second circle...

- circle is equipotent to a square (UK)

- pi + architecture + buildings (Bulgaria)

- what + mathematical + formulas + use + pi (UK)

What mathematical formula don't use Pi.

- constant + value + great + circle (

Really, the circle (C1) is a true great-circle.

- why + is + the + value + of + pi + 4 + in + Indiana (USA)

- pi universe constant (Croatia, Hrvatska)

- value + of + pi + in + rational + form (India)

- fungsi + comparing + two + r + value (ms-opera-mini-beta-android,

- Euclid + rational + numbers + are + constructible ( )

- Mathmatic (Mongolia)

- Chili + pie + IN + maths (Pakistan)

- Maths + actual + value + of + pi (

- new + value + of + pie (, UK)

- tan + pi + accuracy (, Germany)

- pi + imaginary + get + real + be + rational (, USA)

- area + of + circle + cal + "proff" (, San, California, USA)

- proof there is no formula for constant pi (, USA)

This is true. Because the bases are only from ratio and construction.

- Pie + accuracy + to + required + values (, India)

- pi + accurately + changing (, Michigan, USA)

- dakhiometry (, Japan)

- in maths pie is a unique solution (India)

- mathimatical + pie (Ethiopia)

- Historical + Development + of + Pie + and + its + Accuracy + to + required + values (India)

- practical determination of pi (South Africa)

- pi + and + circle + relationship + philosophical (Israel)

- Robes + Dakhih (Iraq)

- THE + VALUE + OF + PI + IS + 3.1415 + HARVARD (Mexico)

- pi-resolution modelling (, Poland)

- historical development of pie and its irrational accuracy to required value (India)

Sorry to tell you, that for the Dakhiometry the Irrationallity is only from Mathematics Ignorance due to its false belief on Artificial Numbers system.
It is time for everyone to be abble to rcognize that all the Dakhiometry proceed on Spatial Language using only Spatial elements. If one was formated by Old Bad Mathematics Dogma he will still remains ever in the Nothingness as irrationally pious. It is useless for him to acquaint the Dakhiometry Spatial Constant.
A Length is for ever a CONSTRUCTIBLE THING !!!

- squaring + the + circle (Czech Republic)

- irrational accuracy of pie (India)

This the real meaning of the irrational term.

- invention + of + pie + in + maths (India)

- value of phi the best solution (Thailand)

- phi + pi + and + e + design (Netherlands)

- mathamatician + and + geomatrical + symbols + and + name (Pakistan)

- proofs of "teh" value of pi (

- circles + theorems (Lybia)

- pi value of Australia (India)

- What + is + the + new + value + of + pie (

- what is the pi value of Australia (India)

- proof squaring the circle (Thailand)

- how can I write algorithm of Pisagor (Turkey)

- squaring + a + circle + formula + in + China (India)

- formula + of + new + eritrean + theorem (

- squaring the circle proof of impossibility (Germany)

Impossibility of Squaring the Circle is from that Circle and Square can NEVER be supperposed together according to the euclidean axiom on geometric equality for figures.
This not due to the universal Equality Principle but to bad method from false concept on Equality due to the ideology of a Geometry built in the Nothingness. Thus, the fundamental real Absolute Space of a Whole is there quite ignored. Therefore, Geometry is dummy empirism science. The Supperposition-of-figures is precisely a mechanism drawn from epirism practises.

- eritrean + theorem (, USA)

- how + can + you + prove + that + pi + has + a + corresponding + unique + location + ont + the + number + line (Malaysia)

- RECIPROCAL + SQUARE + ROOT + PI (Netherlands)

- step by step procedure to approximate value of pi using only a perfectly straight stick (, Oklahoma, USA)

- is pi rational (Hungary)

- find + the + value + of + pie + that + logically + follows + from + this + assertion (USA)

- value of pi till now (United Arab Emirates)

- pie 3.14 incertitude error (, Canada)

- why is knowing the value of pi to high precision so important (, New York C, USA)

- squaring + the + circle + architecture (, California, USA)

No man's dicourse can traduce the equivalence on what are the property of the universe space.
Only spatial architect can discover though constructions how the space was gone in transformation.
In Dakhiometry, there are more global precise and simple constructions according to basic cirle properties showing how:

The squaring a circle construction was actually NOT A LOCAL EVENT.

The truth is:

The Squaring a Circle happened as a ONE UNIQUE UNIVERSE CIRCLE going SIMULTANEOUSLY in PARALLEL-Transformation, adding to its Isotropic aspect the Homegeneous one for the fulness of endless construction in the whole universe absolute space

- circle + diameter + from + square + corner + circumscribed (USA)

Actually. With inscribed circle in a square, it can be state that "equivalent circle is from square corner" and also its reciprocal as "square is equivalent to circle by its corner distance from the circle"

- indian + attempt + to + find + value + of + pi (India)

This shows that the current Mathematics is still remaining in their artificial and false millenary Number system. What ever will be the numeric Pi value, it is necessary not excact and false due to the false concept from ideology of Numbers.
Give to the Dakhiometry Spatial Language a length. Then, from there any spatial SUCCESSIVE construction of figure of the whole universe will be necessary and wholy the exact an acurate one.
Mathematics conservatism can never use the Dakhiometry result as a valid new Mathematics trick. What is false can never created a single one thruth.

One may note that in (n) SUCCESSUVE CONSTRUCTION, the final error (epsilon) of the necessary irrational numbers will increase to (epsilon)n. While the Dakhiometry spatial construction is done according to the point-to-point representing the immutable matter element. There, the precision is directly to the one-elemental-point of matter. Aside man's anthropomorphic fantasy, in the universe there is nothing else than a concrete elemental matter as a point of spatial location.

The current Trigonometry is an unexcact system. The real accurate and exact determination of Angle need the Spatial Language use. It is because only this method can use spatial element to determine what is angles as the true circle property. The half-cycle sinusoide is a true parabolic function and was proved by spatial construction with the True Length Constant. There, it needs to use the co-called Pi not with its cumbersome numeric value. But it needs to construct them with the Spatial Constant LENGTH currently denoted by the millenary imprecise Pi.

However, if there was some conservative optimistic transition period between the Old Mathematics to the Dakhiometry scientifc language then, it is useful to determine an universal MORE-EXACT numeric value for the current Numeric-Mathematics. A rational exact science has not to choose between a less or a more exact value. However, one should consider that it is only a temporary convention if a more true science will be the aim for a futur human's true science.

- Colorado + university + mathematic + parabol + animasyon (Turkey)

- process how the value of pie was get (Philippines)

... a human's adventure in so long duration.

- Chilipi + maths (

- Texas pi 3.1415 apple-os school (Germany)

Exactness and precision in Mathematics should not be dependent to particular interest. Conservatism about such consideration is necessary factor of science conservatism. Without science universality there is only dogma retardation.
It is why current Mathematics have no more access on how to determine precisely Angular space, Volumes, Aeres, Mass center of any Form,... and more fundamental and useful necessary knowledge.
I had given sufficient difficult wellknown problem solutions to prove that the current millenary Mathematics is quite innaccurate. But there are more deeper inside light on how a true rational exact science is possible. However, knowing that most of people prefer their usual comfortable dogma I am in conscience that most of solution given in this web site are transformed as Triscks for the curent generally incorrect Mathematics. It is why fundamental knowledge of the Dakhiometry isn't still not developed here.

- +pi-airgun + precision + ref (Russian Federation)

- The historical development of pie in measurements (

- space + logic + density + for + circle + to + square + transmutation (India)

Density of reasons for circle to square transform, is composed by a long series of basic reasons deducing from each other.
For example, this circle to square transform may be spatialy constructed in Dakhiometry by ratio method between the circle and square figures. This is also a fantastic clearly property of the space when one is used with the Spatial Language, the True concrete language of the Absolute space. The old Géometry that is only a mechanism of finding methematics-tricks, has nothing to do with this true scientific language. This latter is the one necessary internal property of everyone, that however was killed by the millenary practice under Geometry dogma.

- how can mathmatical number pi relate to clothing industry (, Canada)

It is interesting. May be because most of object clothes are from circular forms and particularly with circular movement around its center and clothe are defined and constructed on planar text material.

The Truth of the Dakhiometry science

Everybody have to forget their usual Archimedes' Mathematics Pi Dogma. Persisting in stating the simplistic Mathematics obviousness, generally one stays in the misunderstanding of what are related about the present Dakhiometry texts.

Resolution of the Squaring a Circle is really the root resolution of the Universe Beginning. There was really an EVENT OF BIGINNING OF THE UNIVERSE CONSTRUCTION. So please try to get a better understanding on this next Dakhiometry Fundamental Law:

The universe construction Basic Law:

The Beginning of the universe Construction is the rational Fact of clearly Solving Rationally and defining any matter Form by their Aera and Volume quantities what ever are they from Circular or Linear or in both types.

This is the meaning of the beginning event in the universe absolute space to get fully in the fulness of its isotropic and homogenous properties.

Rational construction is done by interaction of matter with the capacity of being related between them in defined relationships. For example, Solving the Squaring a Circle is the beginning of:

1) - On the basic Planar two-dimensions, Squaring a Circle is the root event of Construction Beginning starting from the universe Permanent Structure. In the continuation on Three-Dimensions, Cubing a Sphere is the direct consequence also resolved in Dakhiometry.

2) - Knowing rationally these basic laws, defining any Aerea and any form Volume are the direct consequences. They are needed to define their necessary Mass center property.

3) - Universe Constructions can then be done by Rational and reciprocal Matter Transformation of Form multiplicity.

So, it is asked to those who maintain their belief on the old Archimedes's Pi, how can they do to know not only precisely but with what method are they proceed with to resolve the Squaring a Ssphere and how do they to define precisely the necessary need on Form characteristics both in theory and in technology?

- whats is pi in math and in portugues (

- squaring + a + circle (El Salvador)

- .pi want to learn to speak chi, the local language of Ghana (

- what is dakhiometry (, Oshawa, Ontario, Canada)

Being realistic, the Dakhiometry no more than a curiosity but it's still a non-existent thing.

- proof + that + pi + is + rational + on + a + calculator (, UK)

- e + square + life + of + pi + show + time + for + 2 + december (India)

... 2012

- human + transmutation + circle + diagram + dimensions (, USA)

- cululati + piu (Greece)

- how + to.+ find + accure + pi + value (Slovak Republic)

- how to find 3.14 pie in a circle Hilbert's axioms (Philippines)

- Pakistan and the value of pi (UK)


- circling the square and squaring the circle and consciousness (, India)

Consciouness can be extended more larger.
With the knowledge on circle, where are originated the Homothetic relationship or what was known as the simplistic Thales Theorem, it can be prove simply the squaring a circle equality. This means that the squaring a circle is no more than a homothetic transformation of AERAS. Fantastic spatial relationship isn't?

- rational value for pi (USA)

- Egyptian + formula + for + pi (, USA)

- grafik + pie + atmosfer (Indonesia)

- what + is + the + value + of + pi + to + the + egyptians (, Red Deer, Canada)

- what + value + of + pi + did + Ptolemy + of + Alexandria + figure (Canada)

- short + pi + formulas (Romania)

- historically who came up with the most accurate description of pi (, USA)

- the + most + inaccurate + value + of + pi

- pi + 1 000 000 000 + digits + full + size (, California, USA)

Fantastic technology on accuracy!

- the + evolution + of + this + technological + invention + allows + us + to + calculate + the + value + of + pi + to + 10000000000000 + places (USA)

Fantastic go ahead!

- why was greek pi choosen to represent this value (

In Anciant time one have only practical means to define the usefulness of circle measurements. The usefulness of a circle measurement is at first applied for defining a mechanical wheel.
So, measuring a wheel is also measuring its rolling track length. Therefore, it is useful for conceiving a wheel to know its Track length as a function of the it Radius. The circle Track Length was denoted by Greeks as the periphery of a Circle or its PI-remeter.

It was why Euclide an Archimedes defined and denoted the proportional factor (Pi) between the Perimeter and its Radius.

It is why the mathematic Pi is alway focused on the How-to-define the Length of the circle Pi-remeter.
The Arhcimedes' process of comparing by exhaustion a Circular perimeter with a Linear polygon was then no more than originated from a Mathematics still using mechanical concept for accessing to the 3-D Space.
The direct comparison BY CONFUSING AND OVERLAPPING ACCORDING TO THE EUCLIDEAN DEFINITION OF EQUALITY applyed here for a Circular-line with a Linear one is Mostly difficult.


The Impossibility of the Squaring a Circle and of the Angle-Trisection, anf The so-called Irrationality and Trancendental of Number, are due to this next reason:

The millinary man's ignorance on the universe laws about the ABSOLUTE STRUCTURED DISCRETE MATTER.

Here next is precisely explicited the consequence of

applied to resolve the Squaring a Circle.
One may note that is is the result from a True Rational METHODS and not from some hazardeous manipulation on figures as it is concerning for most of Mathematics Theorems.

Note that it is also a true basic rational science Spatial Language Method. This whealthy view point is also repeated when applyed for resolving clearly, simply and wholy the Angle Trisection.
More further, many physical phenomena may be clarifyed with such universal understanding of Matter.

- pi and nothingness (USA)

- pi + and + irrational + numbers (

Actually, empirism is from Nothingness of anthropomorphism view point on a Pi-remeter rolling wheel.

- circle + impotent + therom + proof (India)


- NEW + VALUE + OF + PI (India)

- pi is rational number (Malaysia)

- HOW + TO + FIND + AND + PROVE + PI-VALUE (Egypt)

- what + do + Dublin + doors + and + pi + have + in + common (

- the + most + accurate + value + of + pi (Tanzania)

- squaring + the + circle + k12 (, Texas)

- latest + researches + on + value + of + pie (

Certainly, it's a Fact.
On have now to consider that the research horizon will concern the different aplication aspects when one will get more understanding on such Pie Constant. The Pi is not only concerning the Circle characteristics. It is really the universal matter Construction Factor that allows the space unity between its Linear and Circular aspects for matter relationships foundation.

The most practical problem is to know that this Constant is a key for understanding the diffrent Form Volumes and then used for mastering their Mass-Center.
This is the true modern vast practical consequences from this basic Spatial Constant initially considered by the Anciants as simply used to resolve the Circle perimeter. This was only to define the First application problem meet by builders: How to get a good measurement on circles for conceiving big monuments.

- pi + and + the + univese (

- Mystic + rational + pi (

- algorithm calculate pi in painting (, Pennsylvania, USA)

- squaring + the + circle + proof (, Greece)

- descirbe + how + the + computer + has + contibuted + to + the + teaching + and + learning + of + mathematics + in + schools + under + structure + and + functions + of + parts + of + the + technology (USA)

The Numeric technology contributes effectively for a great enhancement of Mathematics developments.

- reasoning of value of pie (, India)

- proof the value of pi in circle method (India)


- what is the actual value of pi (Nigeria)

- what should I do if I want to be a matheamtician (India)

Genuinely, to be an efficient mathematician, one have to make a very superman effort to forget that "One uses to have his mathematics little ways for tricks and recipes".    :-)

- pie + accuracy + to + required + values (

- inventors of pie value (India)

- proofs for the exact value of pie (India)

- accurate value (Philippines)

- historical development of pie its irrationality accuracy to required values requirements (, India)

- squaring + a + circle (Pakistan)

- unit + of + pie + and + it's + accurate + value (UK)

- can + value + of + pie + b + return + in + the + terms + of + rational + number (India)

- pie + accuracy + to + required + values (, India)

- deduction of value of pi (, India)

- deduction of value of pi using activity(, India)

Actually. It is important to know that no man's technology can't rationally make up a circle.
Only through the natural space fact of circle-to-square transformantion that one can hope to know the circle characteristics: "Circle practice makes perfect"

- (

- equivalent square of a circle formula (South Africa)

- squaring the circle solution revealed (, Texas)

- pi + calculator (Taiwan)

- nail + designs + Trinidad + pi (

- squaringcircle (Finland)

- pi + in + rational + form (

- comsouth + vercatel + compas

- formula del pi (Mexico)

- pie is defined as a ratio of circumstance (say) of a circle to its diameter (say) that i pie c d. this seemes to contradict the fact that pie is irrational. how will you resolve this contradiction (India)

From millenaries Mathematics is defining the Quantities of reality by using artificial Words symbols. From there was creted the Numbers for counting realities quantity. Property of Numbers is then no more than the one of conventional creation of talking words. The default of such system is that any precise quantity of reality can not be precisely defined by a given precise Number. Such imprecise practice for quantity symbols produces the discontinuity of quantity representation from there was invented the Dedeking Cut. This latter is temting to define the true continuity of representing quantitie. A such discontinuity for quantity representation produces then the Mathematics Irrationality of Numbers. This is no more than to recognize that Numbers is no more than an artificial means what ever the different method tempting to define the quantity continuity.

Therefore the Irrationality is no more than to underline that Mathematics is producing a Bad practical process according to that natural continuity of the natural quantity can be never represented by the necessary discontinuity of man's language words. The Mathematics belief on Irrationality is by itself a contradiction to and another Mathematic concept on Infinity. It is because that Infinity is no more than an indefined No-Thing where quantity cannot be defined. It is to state that natural quantity is strictly from Continuity process et not as the inescapable Discontinuity of Language Words.

The irrationality of the Anciant's Pi suffers from an another big Ignorance that is the the One about the circular form. A Circle defined by a compas-mechnism is also an another No-Tning invented by Mathematics to hide the Mathematics ignorance on the universe Circularity Fact. Thus, even if in Mathematics there was invented a prcise definition system another than the Numbers to describe the continuity of Quantity, the fact of ignorinhg the Circularity imply that necessary, a Mathematics Pi is nécessary an irrational Thing.

It is because ignoring what is the Circularity of a circle, then a circle arc is necessary an ignored Thing.

The Mathematics Irrationallity is finaly specific to the Mathematics ignorance that the universe Space is not the Nothingness by formed by Structure of Discrete Spatial Locations. This the fundamental base from there knowledge on the universe should be necessary built.

It is why, quantity should be decribed according to the spatial Elements as Points, Lignes and Curves.

Note that Mathamatics believes to that the universe is Infinities. Therefore, as Infinity is a No-Tning its property is at least the famous scientifc Continuum.

However, the universe Space is a whole of Continuity of Discrete locations for any Matter realities definitions. And whatever is the Form, this latter is necssary precisely defined by the necessary continuity of its total number of points. Thes points are the precise absolute quantity of any form.

Finally, what about the Space Continuity (but not the Continuum one)?

The Continuity of the universe space Locations, has a Dakhiometric root definition as:

One Location has the property of being both characteristics as a-Preceeding-and-a-Succeeding one

When one define a given Point (P), this definition necessary define precisely any Point-between-two-other-defined-Points. That is the fundamental definition of the universal Continuity of matter or ITS PRECISE TRUE QUANTITY Definition.

In conclusion

Numbers are from primary Mathematics of man being till with a primary science.

Now about the problem of the irrationality of Pi, this is only a millenary Mathematics chimera.

And this so called Pi, is not described in this present-text. Here it is defined the universal Space Constant that allows the direct transdormation from a low scale circular line into an Infinit circle Arch. It is because there is NO STRAIGHT LINE in the circular structure of the universe.

In Space of Discrete Locations, there is no Irrationality. The impossibility of the Squaring a Circle was a Mathematics Impossible Problem because of the Impossibility of a Irrationality Numbers of a false Counting system.

Now, why the Dakhiometry Space Constant is not an Irrational Thing but a real Precise Quantity?

It is because, this Constant is constructted according to the spatial Construction where a point of a segment, is a Discrete Point of the universe Space Location situated ALWAYS between a precedding an a succeeding ones.
Before or after this Defined Point, there is no possible mystic Dedekind-Cut.

- "latset" + value + of + pie + discovered ++ now (..)

- new ways calculating pi (Australia)

- development + historic + values + of + pi (Egypt)

- how + to + prove + value + of + pai (Nepal)

- mathematical pi value solution (India)

- Great + Artworks + in + geomatrical + maths. (

- i + take + big + numbers + transmute + them + then + calculate + their + low + bearing + tangeants (UK)

- squaring + circle + father + son + evil + ghost (, Sweden)

- Australia + golden + constant + pi (Ethiopia)

- exact value of pai (India)

- value + of + pi + remains + constant (India)

The Mathematics irrationallity problem

- pi is the ratio "pf" circumference + to + diameter + of + a + circle. This + seems + contradictory + to + pi + is + irrational.+ how + can + we + solve + this (, India)

1) - Irrationality is an artefact of the Number system on that Mathematics are founded. The problem of irrationality is a specific problem inherent to the Number as conventional and artificial talking language. This latter is not deduced from the true and natural space language the alphabet of wich is Point-Line-Curve.

2) - In fact, the Space reality rest only on the Point. Therefore, Line and Curves are formed with Points. And in the universe Discrete Matter Point is the Elemental matter dimension according to the uniqueness principle. There is not one Not-a-Point in the universe. This is the basic property of the Spatial Language.

3) - It is why intersection between Lines and Curves is necessary a Real universe Point. And this Point is necessary inherent to any concrete univers reality and never from man's dream.

The Dakhiometry is based strictly on the use of the spatial language as the the true representation of the Space Realities.
The Pi length is determine as defined point to point line. Therefore this Pi length is fully defined as quantity of spatial Points. the Squaring a Circle solution is here from pure Spatial Langauge resolution. The Pi is then always quite defined quantity of Points in a defined Segment of Length.

It is there no need to invent some tric and cooking recipe from Mathematician nightmare induced by the millenary artificial Number system.

The Irrational Number is strictly from Mathematician false method to define Quantity of matter. And one may note that any irrational Number "proof" is done with Number calculations. That is to tell:

With a Given Scientific System of calculation tool production, one can never prove with these same tools, any contradiction in this system.
It is to tell that irrational Number are strictly the internal generation product of the millenary Artificial Number System

I propose to Mathematician formed from Number System, to resolve the true possible Irrationality in the univers as follows:

[Figuring out the so-called Integer Numbers)

The Basic Irrationality Problem as,

How to prove that from real intersection of Line or Curves, can results a No-Intersection-Point

The so-called Mathematics Irrationality chalange is to prove, by construction, that there are in the above diagram one Quantities at least, as one Not-a-Point-intersection.

If there was rationally some Not-a-Point-intersection then the Irrationallity is a valid problem!
In the oposite case, the mathematics' usual Thales theorem is false. Therefore, one should in a hurry cancel the Mathematics Irrationallity Ideology that deal ruthlessly with Sciences.

If being rational, the DUTY of Mathematicians of irrationality is to prouve this problem Fact of Non-Intersecting Point for figure.
A such proof should be really the true proof of the validity for Irrationality , the Nothingness, the Spatio-temporal validity and the Nothingness Facts !!!
However, at first, if a Not-A-Point-intersection is prooved it will necessary be a false one!

The reason is that a Nothingness can never be proved as True or False. Mathematics havn't no principle as base to perform such True-or-Not problem resolution. It is because man's Believes can never have a rational access according to that Believes is a man's of no reason-behavior.
Therefore, proving the Not-a-Point will be transformed into the result of an contradictory eternal Impossibility-Theorem. Note that it is excluded from there the Euclide's Infinite Line because it is only from Euclide's chimera.

And also according to the Dakhiometry, it can be proved that:
From any univers Point, there is a Least-Distance from this Point to a system of another different real Points.

I am sory,
because Mathematics of Numbers fact is a proof of Black Hole reality and inversely.

- formul + pi + geometric,
- pi + are + rea + geetrik (, Greece) - pi + are + real + geetrik (Greece)

- squaring + the + circle (Guatemala)

Important Note about the Squaring the Circle

The so-called Pi of the Anciants is only a simple annecdotic fact of man bored by the unknown displacement Length of a rolling wheel... according to that they was ignoring the Circle

The main result
of the Dakhiometry Squaring-the-Circle is:
To prove that the universe space is being Absolute !

Any point by itself and any point relatively to another ones of the universe is then absolutly defined. This is the proof that the universe is a Whole and more,...

The universe is The Unique Whole!

Amongst another consequences, Mathematics Numbers, Geometric postulates, Infinities and Irrationallity are Mythes!

It is note also that the Absolute universe Space is proved by an another method using directly the Circle specific property. It is done using the Least-Distance property between one-given-point to a set of another points in the whole absolute Space.

In summary.

Necessity of the physical Absolute Measurements

There are two means to prove the universe Space as being Absolute:

I) - The Absolute Space means that

Any-location of the universe Space is always in determined relationships with another set of locations in the whole universe space.

II) - The Absolute Space means that from any-location of the universe Space one can measure its distance from a set of another locations in the space.
In this method the problem cannot be to determine the longest nor to determine the distance equality.
It is because Relativistic Dependence can never be the reference for Absolute Property Conditions.

Therefore, measurements should be also from absolute processes.

One can logically determine only the Shortest distance from any determined-location to a set of another ones in the whole universe space.

If this latter statement is difficult for the understanding of usual mind formed by Relativity as the Dynamics and its modern derivatives ones, I give here an simple example using the current welknown Number system.

So, do you know why Numbers begin only from (1) (but not from Zero. Because Zero-represents-No-Quantity (the Zero is not-a-number)?

The basic answer is that concretness of Quantities should necessary begin from a concrete "One-Quantity"!!!
Therefore, there is no possible Quantity that should begin from Biggest Quantity because the Bigest is alway refered to a Lower one and inversely! Any Quantity should be refered to an absolute Quantity One. It is why the true universe Quantity is necessary from the Discrete Matter represented by an ABSOLUTE ELEMENTAL Discrete MATTER, the Dakhion of the Dakhiometry!

The Euclide's Line that begin to grow from Infinity and is "restricted" between and by two Infinities is necessary a from usual man's chimera !

A true Line as a succession of the Space discrete Locations should begin necessary from ONE Real Elemental Matter.

It is why to determine the distance between a physical point to another points, The Absolute Reference should be based on the Shortest Distance. It is because in such situation, this Shortest Distance represent an absolute reference.
In this cas, the Shortest Distance plays the role of the UNITY of this measurement system!

Formula Determination for Pi

Dakhiometry Calculator applied to Pi formula: a neat solution.

- since + we + define + pi + as + the + ratio + of + the + circumference + of + circle + to + its + diameter. this + seems + contradiction + + to + the + fact + that + pi + is + irrational. how + will + you + resolve + the + contradiction (India)

a) - Mathematics is sūrely incompatible with &qot;seem"
b) - What is the Fact of "Pi is irrational". This Fact should be prooved by reason and not by conventional consensus of some group.

1) - So it should be interesting that mathematicians try to prove according to reasonning that the squaring a Circle is irrational.

2) - If this problem of squaring a Circle is not irrational, then the sa called problem of Irrational Pi is a false problem.

3) - I have not interested to prove that belives is irrational or not. So I can't resolve what is matter of man' believes.

One should see that Pi is not originated as the ratio between the diameter and the circonference of circle. This belong to the Anciants's believes when they can't have some understanding about the Circular property of the universe spacewhere where they see as a Nothinness.

Contradictory to these Anciant's believes, this Ratio (Primeter/Pi) is SIMPLY from a secondary-consequence of the Squaring a Circle.

In fact:
The Squaring-a-Circle proves that the Ratio (Pi = Perimeter/Diameter) is from empirical irrelevent technique tempting by the Anciants trying to resolve the impossible problem of a circle perimeter measurement.

On should note that the Length "Pi" id only possible by obtaining the Ratio-Of-Aeras. It is why to get the Length Constant Langth, on should resilve the Mythical Sqyaring the Circle. Mathematic can NEVER resolve the Squaring the Circle and more resolvin the compareason bt reasuring the Diameter of circle. The Basic Reason is that MATHEMATIC IS FOR EVER IGBORING THE CIRCUKARITY, therefore, the Diameter of Circle. This ignorance is the source of the Impossibilty of the Mathematic to resove the Squaring the Circle!

This impossibility was inherited from the Anciants by modern mathematicians that ARTIFICIALLY and IRRATIONALLY CREATED The Impossibility-of-Constructing-and-Algebraically-resolving the-Squaring-a-Circle.
Ignorance should not be a base to be used to establish Irrationallity Ghost for Dark Science ! We are there no more practising Rational Science.

Now, the Squaring-a Circle resolved and therefore, should destroy any believes on Irrationallity in Mathematics.

- Impossibility + of + squarring + a + circle + with + ruler + and + compass (India)

- pie for maths calculation (HongKong)

- Pi + Math + Formula (

Actually, the Pi Formula can be built by reading directly on this next figure.

- Boston + MA (Massachusetts)

- pie + for + math (


- The + begining + and + nature + of + mathematics + and + distintive + discipline (

- pi + equations (

Really, this structure of the Space is concretly and fully telling the Pi equation. One have only to read it.

- elementary + math + pie + charts (

- how + to + rotate + the + co-ordinates + of + image + by + 90 + degree + in + plane + aroung + any + fixed + point (Korea)

- pie accuracy to required values (

- new pie value solutions (India)

- aims of education as "pastulated" by philosopher (..)

- PIE + formula (Autralia Aotearoa)

- proof of pi (Turkey)

- pi accuracy to required values (UK)

- what + is + the + easyest + way + to + find + out + pi + value + using + circle (India)

Actually, the squaring-circle for kids...

In fact there is an another basic fundamental way (not yet exposed anywhere) to get the squaring Circle by simply using ONLY and Uniquely the Circle as fundamental tool.

Fondamentally, the universe Circle is pregnant of Forms!

It can be get when one is familar with circle property and also when one is convinced that the universe is structured strictly by Circles.

Then from there it can be seen that the Beginning of the Universe Construction happens only from Circles and not mixted with Lines and any another form. Because the Beginning of the univeres is starting from FORLESS Universe of Matter. Therefore, only from Circles are born the first matter forms denoted as the Squares.
From there was setting the linear aspect of the universe Space.

MAy be, the Circle is NOT a FORM.

It is why the Mathematics ignores what is a Circle. The Platoo's Compass is not a Circle but only a mechanism as it was currently used as tools by the Anciants in Mathematics.

Really, the Dakhiometry can prove fully in "Top, Bottom, Left, Right, Front, Back, Inside and Outside View", in Virtual and Real aspects of this Squaring Circle as the Passage from the Permanent Circular to Homogeneous and Isotropric properties of the universe Space.

The Squaring the Circle as the Beginning of the universe is not and utopia.

This solution of the Squaring the Circle starting only from the Circle was not exposed here in this web site because it is difficult for usual mathematicians to have somme clear insight of the pure circular property. The squaring a Circle will then be seen as a true JOKE for Kids.

However, as according to the Impossibility Law, the Squaring the Circle by itself may appear as a Joke. And with its marvellous new aspect of the true sicky Dakhiometry Space Langage it will be seen probably by the current conservative method of mathematicians as an incredible Nightmare!!!

- proof for circling the square (

- pie accuracy to its values (, India)

- Archimedes + and + derive + its + formula + of + pie (

- general - form - of - the - equation - of - a - circle - solver (

- proof + of + pi + value + using + triangles (South Africa)

- in + circle + pai + equal + to + circumtences + divided + chord + which + contradicts + pai + is + irrational + how + can + we + prove + pai + irrational (India)

The Irrationality is simple from MAN IGNORANCE

1) - The diameter (D) of a Circle is not any circle-Chord.

2) - Searching to characterize a circle, mathematicians tempt to define the "number" that may characterize a given Circle. This:
Pai = Pi

a only FROM EMPIRACAL process on pratice when one tempted to define practically the distance of a wheel when this latter had doing one cycle.
This is a quite empirical manner of mathematician believing that exact-science is simply to get measurement according to SIMPLISTIC method as:

"Equality = Figures supperposition"

This is a grave fault from Mathematics millenary iggnorance!

3) - What is precisely this mathematician-serious-mistake???
IGNORANCE OF MATHEMATICIANS is simply to ignore that Circular-Line is from another Property of the Space quite differently from the STRAIGHT-LINE one !!!

This Mathematician Thoughtlessness when the problem is to define a Circle, consists to drives them the usual BAD empirical process of:

b) - The only accessible circle Dimension is obviously its greatest dimension denoted as the CIRCLE-DIAMETER.

This Mathematician IGNORANCE remains until now in the Modern Time, where Mathematicians are still dogged by their bad luck ignorance so that they are carrying a darm by the Irrationallity nightmare. Thus, for protecting them from such trifle they invented the Irrationality and the Impossibility of the Squaring a Circle.

The fact is that the irrationallity and the Impossibility are not from the Univers space properties. These bed of sickness is simply lodged in the mathematicians thought.

There is no rational reason that allows to free them from such powerful mysery.

I suggest mathematicians to read somewhere in this present text, where are lodged the fundamental incompatiblity between the Cercle and the Straight-Line. This ignorance is dangerous when one tempts to produce a hight-speed ROLLOING-WHEEL on a plane-straingt surface. This practical dangerous phenomenon is still ignored by engeneer-formed by-Mathematics/Physics.

Now it is my last remark about this Mathematician Irrationallity applyed to the Circle. There are more rational interesting problems to resolve for clarifying towards a better condition for man knowledge.

In summary:
When, according to the Empirical euclidean stating that
""Figures Equality = Figures in Superposition"",
one tempts to associate by successive-points contact between the Circle-and-the-Straight-Line ones then, Man should be disolved into tears.

The so-called Irrationallity is not from the universe rational Space property. It is ONLY from Man's misfortune.

Is there someone for "prove" that an illusion is Illusion?

In conclusion on irrationality and trancendental numbers

All the Mathematics methods rest on the Euclide's Division of Numbers. This is the basic statement that proves why Mathematics BELIEVES to Irrationaliy and Trancendental Numbers as modern mathematicians inherit from millenary numerous believes.

It is because all the Mathematicians' so-called Proofs of Irrationality, are done according to inaccurate euclidean division.
For example, it is according to the Euclides's division method that PRIME NUMBERS is the Mathematics invention.

Prime Numbers and another particularities of Number System are fatal contradictions to the universality principe!

Now imagine that concerning Length thus,
Is there some types of Lengthes characterized as belonging to "Prime-Legnth" property ???
Is there Irrational or trancendetal Length??? No of such oddities as universality facts in the universe!!!

Multi-Strangeness of man's Artificial Number Systems are only from man's ignorance and tehrefore, from man's everlasting Believes!

The Big Contradiction is the property of current sciences:
If one have some understanding on his Mathematics then:

a) - One can never invent the Continuum belief. A simple Prime Number and irrationality is the perfect contradiction of the Continuum Belief. It is because these different pecularities of Number is stating that there is no possible Continuum in the universe!

2) - There is simply a fact that contradict these eccentricities of Number System. Because if there was Irrationality, Prime Numbers and another Number-Things then, the Thales Property is necessary invalid, there will be no regularity in the universe Space, therefore no possible Universal Laws!

3) - These odd millenary inventions of Number System is no more than from Man's ignoring of THE UNIVERSE SPACE WITH BOTH PROPERTIES AS HOMOGENEOUS AND ISOTROPIC!

There is no uncertainty in the universe perfectly defined by the ABSOLUTE SPACE. This latter can be Rationally proved with the Spatial Language of the Dakhiometry !!!

Absolute Space means that any Point-Location in the Space is Prefectly well defined according to the Absolute Space Property.

It is because any Thing is a figure Spatially defined by its points-to-points LOCATIONS in the Absolute Space. In Dakhiometry, it can be rationally proved by construction, that any Point is at Least Distance from a set of another Points in the Universe !


If there was some undefinition in the Space then,

The Fundamental Principe of the Energy Conservation or more generally with it another statement as the Principe of Matter Conservation is not fulfilled.

Therefore, it will apears the Mathematician's Irrationallity and some another numerous millenary mystic inventions. This is the consequences of Mathematics huge Ignorance of Physic Principles according to that Mathematics rests on the belief of the World-in-Nothingness.

Without such basic Principe of Conservation from the Absolute Space, Mathematics is simply a huge "Do as you like-it" !

I) - The Irrationallity is ONLY the one from human error and also to his irrational mind !!!

II) - Science for Life in the universe should be fundamentally and necessary rational and accurate.

III) - Man should cancel all of his millenary Believes.

So if Man tempts to have a talk with some Green I.T.,...
It is recommanded to never do it with Prime Number for having Top Knowing Look as is your Intelliegnce-Top.
That's for travelers-with-long-ears coming from the oposit side of our Milky-Way, the worst possible insult! They will believe that you pick them as new-borns up with a pair of tongs. Be on your guard, E.T. with their saucers may be quick-tempered!
If you are sending a Human Message throughout the univers, don't mention Our Pi under culbersome Numeric Form. But send to them a simple Spatial Figure with the relationship between Circle-And-Square. Only the Universe Space Language is Universal and may be understood by any advanced ALIVE in the universe. Number is only invention of primary human Shrews.
Point, length, curve and their compositions in forms are well recognized by animals. It is because these space alphabets have their own meaning.
It is not the case for the human alphabets where thesz signs have no relationship with their wearing Conventional and abitrary Meaning. The hieroglyph is an exemple for modern aphabets and reciprocally.
Please one more FOR OUR SAFE,
concerning the Heavenly Sky relationships, never mention the lugubrious Anciant's Mathematics Number System.

- yangtzeu (China)

... le Golden-River...

- the + formula + to + culculate + an + area + of + a + "cycle" (South Africa)

- pie + formula (China)

- equation + pi + and + the + universe (, Illinois)

Facteur of thansformation between Circle and Square or Circular into Linear is Basic. It is because the results of matter constructions depend to these mutual relationships. Length, Aera and Volume can be known precisely according to a well precise transformation factor Pi. It is because accurate Spatial Language is the true physical image of these constructions.

- Explain ++ chili + pie + + method + in + mathematics (Pakistan)

- Pie + Math + Equation + In (, Colorado)

- Pratice + makes + "perfact" (Korea)

- the-rational-new-pi-accurate-value-resolution (Gabon)

- The + technique + of + finding + pi + value + in + bangla"

- Pure + construction + in + maths + using + compass + ruler + free + download (India)

- does + the + value + of + pi + have + a + resolution (, Massachusetts)

- what + is + the + mathematical + equation + for + pi (Mexico)

- geomatrical + construction + universal + method (Pakistan)

Formula Determination for Pi

Dakhiometry Calculator applied to Pi formula: a neat solution.

After getting the square (K) from the Squaring construction, it needs to be included into a general space structure denoted as the Dakhiometry Calculator Structure. It is a spatial structure which has the wealthy property of the universe Space Matter.
The Calculator structure consists to create and obtain the matter central symmetry property. It is done by 90° rotation at four times to the square (K) around the center (O) of the golden circle (C1). There the Calculator gives to us, directly and simply any factor needed to determine the precise Pi formula.
In fact this formula is deduced from the rectangle with given sides L2 and L3. There, L1, L2 and L3 are perfectly and simply determined by this structure.
Therefore, there is no problem. The Dakhiometry Calculator had done its job!

The Spatial Calculator is an unbounded wealthy means for many other calclations... if one is mastering the Dakhiometry Spatial Language.

- void + fill + segment (line + L1,+ and + L2)

We can see that a just space structure can determine by itself the needed solution. The squaring a circle is really an auto-transformation event in the space.

With AF=a, BH=c and L1=AB/2
The segment (EB) as:

EB = AD = a = L2 + L3

The calculator structure give directly that L1 is no more than the square side length inscribed in the circle (C) And finally it can be get easily without searching tricks:

       Pi/4 = (a2) / (c2)

According to that, it is directly the side measurement of the transformed circle (C) into the square (K) with this precise side dimension.

- the solution to pi reveals the maximum resolution of the universe (, Canada)

This is a fantastic realistic viewpoint on the universe absolute space. Really, the universe resolve with accuracy each of its elemental matter as the uniqueness of matter Quantity!

- how + to + draw + a + square (Italy)

What is concerning the precise result given by the above created structure?

The calculation done under the algebraic formalism is only for mathematicians that are not used with the Dakhiometry spatial language. As mathematicians know only the Numbers form of Pi, the algebraic numerals is given here only for their best understanding.

Because for the Dakhiometry, the solution to resolve is how to obtain only ONE intersection point between the circle and the transformed square.
Here, it suffice for the Dakhiometry to know ONE POINT, the (P) one. Thus the structure formed around the golden circle (C1) allows to get directly the pont P. Therefore, both the segment PO and also the radius (PE) of (C), is immediatly given as solutions by this new structure.

Therefore, knowledge of the space properties allows to get simply and neat solution, even for the very difficult problem as the Squaring a Circle.

You are informed that the Angle Trisection is also resolved by this type of neat and simple resolution. There is an important remark about science methods:

High science doesn't be sufficient to found remarkable theorems. A high quality of science should be expressed and composed with the most simple method to obtain any problem solutions.

This is not the case for the millenary Algebraic formalism with all its modern complicated formula. Necessary, these latter will soon put the Algebaric Mathematics on the spot, where this science will be lost in its unavoidable growing complications.

There is only and strictly,

Here is the imediate adplication of the Dakhi-Form:


Squaring sphere

In Dakhiometry, it can be known the Surface-Aera and the Volume of a Sphere by Spatial Constructions.

Until now the formula for the Circle and Sphere concerning their Perimeters and Aeras, are found ONLY by trial-Error.

The Dakhiometry can prove rationally by construction, why these formula rest on. They are done according to the Principle of Discrete-Matter. This is done as Matter Elemental Points where transformation of point-Locations obey to the Discrete-Matter-Conservation. This shows the importance of the universal Space Dakhi-Form formula. For example it can be construct POINT-TO-POINT how the Sphere Area and Volume can be constructed point-to-point. It is why the Circle and Sphere can be determined precisely as Perimeters and Aeras by their Form characteristics.

The Dakhi-Forme is not a simple formula for the Old-mathematics Pi. With the Dakhi-Form a sphere characteristics can be constructed point-to-point.
How one can imagine that Matter quantity of the Sphere-aera, is greater than its Volume one ??? However, it is not the case. On this figure the square representing the volume is simply a side of the volume cube.

Therefore with the Dakhiometry, there is no secret about the Curvilinear-Realm in the universe Space. Circle and Sphere belong to rational and exactness constructions.

Let (D) the diameter of a sphere and (DF) as Dakhi-Form-Constant.

Aera of a sphere is:

Aera = (4.D2 . (DF)

Sphere Volume = [(DF)/6] . D3

From these factors,
It can be constructed the reciprocal constructions that determine the Given Sphere of (D) diameter.

From a given Sphere of diameter (D),

It can be determine the Squares aeras correponding to this Given Sphere. Here next represented by the following figure:


These determined Sphere Characteristic underline the basic physical property of heavenly bodies globe:

The ratio Space/Volume of a globe property indicates that a heavenly globe is mainly determined by its perimeter AERA as the maximal zone for complex Matter-Construction. And the sources of its rotation-energy is the property of its Volume.

These globe physical structures indicates that the alive complexity should be situated only on the globe surface.

there is never complex construction (as alive creatures) inside the internal volume of any heavenly body where production of rotation energy is necessary under its extrema plus-or-minus.

Taken the Earth globe as an example,
in the whole universe space,
if there was any ALIVE HEAVENLY BODY,
this globe characteristics, should correspond to the Earth globe dimensions with minor differences!

However, for the Dakhiometry science...

This latter algebraic analysis is for the mathematicians Algebraic Religion Belivers.

Because the Rational Dakhiometry need not so complicate with Tricks and the so-called coagulated Pythagorean theorem.
It consists only to use the Dakhiometry Spatial Method and simply to go directly to this next following figure.
It shows that using the Lam-Ca theorem, the Dakhiometry can perfom easily the division of two aeras as:

       Pi/4 = (a2) / (c2)

And to figure out directly the Space Constant as the:

(Pi) LENGTH and also the ratio (Pi/4) LENGTH

The LENGTH is not a new modern fashion for science change according to different language words. Because the Length is directly used by the universe construction through universal laws to realize this alive universe that we know.

Thus, after constructing the Squaring a Circle process,...
It consists only to determine the universal Space Constant denoted by the mathematicians believers as their empirical and false antique and numeral Pi value value.

- dictionary + of + algebraic + terms + and + symbols (

- Exact + Circumference + of + a + Circle (India)

On this next figure, the square (L2) perimeter is the exact measurement of the Circle (C) perimeter.
It is equality not according to the Euclide's empirical Superposition but by Real Rational Transformation of figures.

- "" (Taiwan)

- SCIENCE + Quadrature (, Virginia)

- using + inverse + square + law ++ to + veryfy + magnet-magnet + interaction + force

- algebra + + whatis (

Absolute Space Constants

Therefore, all what is needed to rationally determine the mathematicians' Impossible Squaring a Circle needs only these present short paragrahes.

It is determined the squaring a circle with both criterions as Equality of Aeras and Perimeter.

We consider here the space property where a Circular Line can precisely correspond to a side of a square.
So what about the anciants experiences about measuring a wheel perimeter with a circle rolling on a plane. Doing so one can get a coarse approximation of the wheel perimeter.

Now, in modern time we have to know what about the Mechanical behavior of a rolling-wheel with high speed of a car or a motorbycle. The question is:
For a car with a perfect wheel adherence, do its Perimeter can really unfolding its perimeter exactly for an equivalent Line?

A wheel is a material system. Thus, a driving wheel is used to displace a car. This seems a such device is a perfect invention used to get a displacement in distance. But without considereing the friction,

In practice, does a Circle perimeter correponds to a stright Line?

- unbalanced wheel motion from axle induced oscillations (Nancy, France)

Even with perfect construction of circular driving-wheel, the oscillaions are produced not only according to imperfect circular wheel but even it does with a perfect round perimeter of the wheel:

the oscillation of a driving-wheel is due to the fundamental INCOMPATIBILITY of CONTACT between the rolling circle and the Straight-Line-Distance!

THERE IS NOT successive-adjacent POINT-TO-POINT Contact between Circle-Perimeter and Straight-Line. It is why,

The Euclide's statement on the so called "Equality Principle by Superposition of Figures": is simply from Empirical Observation Science.

It is to tell that what was observation from experimental process can never be stated as Rational-Principle. THERE IS NO POSSIBLE MEASUREMENT BY ECLIDEAN SUPERPOSITION between these two types of the Space Forms!!!

It is because,

The perfect contact is theorically impossible to be done experimentally between the Line/Circle contact. Therefore,

A perfect circular driving-wheel on a planar surface is a continual boucing phenomena as like an unbalanced-wheel. This may be clearly sensitive when the wheel rolling-speed is enough high where developed energy is high.

The Impossibility and the Irrationally of the Squaring-a-Circle in Mathematic is from this unknown but real fundamental incompatibility between Circular-and-Linear type of the Space Forms.

It is from there thet was the basic Archimedes's unsuccess when he tempted to compare By superposition-measurement Polygons and Circle perimeters for determining His Pie.

Now one can have somme key for understanding why

the Dakhiometry can perform The Squaring-a-Circle according not by Measurement but by determining a real Matter Transmutation Process of Figures.

The secret or mystery of the Dakhiometry Squaring-the-Circle rests on the Basic Knowledge,... according to its foundation done on the universe Principe of Discret-Matter !!! ...

And not on the so-called Einstein's CONTINUUM and the Anciants' Space-as-NOTHINGNESS!
It should be ubderlined that The Euclide's Equality-By-Superposition is a process generating from the Nothingness Continuum Belief !

In summary:


- dragster + car

Dragster cars illustrate the driver wheel behace as bouncing system during high level acceleration.
It is the case when one try with a car to achieve the record. In such driving and non-driving wheel in high rotation the wheel behaves only as powerful bouncing system.

1) - Does a circle mechanism a true perfect system for transformating its perimeter into corresponding linear displacement?

2) - One should consider it as a whole physical system as a mechanical one in its motion behavior.

3) - Each point of the wheel perimeter in motion have its own inertia effort.

This next figure shows the repartition of different efforts on the rolling-wheel perimeter. Each point of the wheel is not under a tangential effort for producing a correspondent linear distance on the road.

A driving wheel and also a not-driving wheel have this same mechanical inertial behavior.
This shows that the usual famous tangential effort of a wheel is not the truth.
In fact considering the theorical correspondence between the circle Perimeter and the Straight Line, a rolling-wheel behave with a dissymetric effort during it rolling-motion.
At the contact point (O) between the circle and the road there is a rending effort action on the Circle perimeter.

Finally a such mechanical behavior of a rolling-wheel explain why at a high rolling speed there is no more wheel adherence on the road because there is no more effort of the wheel perimeter on the road surface. This not concerning only due to the aerodynamical effect.
Therefore, with a such behavior, a wery high rotation of the wheel explain why a car and a motorbycle are limited on the speed they can perform. More the dissymetric effort produce a cyclic vibration and produce resonnances that opposes the wheel addherence on the road even with heavy load. This capabilities of a rolling-wheel explain why at these extremum speed there is no more road-holding and accident happens.
Also, it explains why it is difficult for a car to escape from the mud or snow when its wheels was getting stuck.

Note that these mechanical dissymmetric behavior is also applyed to any mechanical gear and limits their rotation speed possibility.

- perpendicular + lines + with + their + symbol + notation (

- Table + of + Mathematical + Symbols (

- tabla + de + simbolos + matematicos .(.)

- Table + Of + Mathematical + Symbols (Michigan)

- pi + value (Philippines)

- mathematical + symbols + dictionary (

- pure + construction + in + mathematics (..)

- who + created + a + formula + to + rapidly + caculate + the + value + of + pi (Canada)

- inventors + of + pi + in + maths (VietNam)

There was numerous particular ones all along millenaries.

- antique + mathematics (

- squaring + a + circle (Hong Kong)

- ancient + stone + circles + Jordan (Colombia)

- transformation + from + square + to + circle (Taiwan)

- squaring + the + circle + mystic (, Portugal)

- golden + rational + circles (Jordan)

- rational + pi (Germany)

- pure + construction + in + mathematics (India)

How the Dakhiometry-Calculator allows
to get so simply the Space Constant value?

- human transmutation circle golden ratio (USA)

The 0.78... is from a constant golden ratio utility.

- How + do + I + find + the + square + root + of + 0.78 + on + a + line + (geometrically) (, Nevada, USA)

You are hot on the scent.
In Dakhiometry spatial language, any calculation on a length can be performed exactly by construction.

Dakhiometry Theorem:
This theorem is Practically done as follows:

One can get directly by construction, the basic ratio length:
Pi/4 = .78...

a) - From there construct a circle of diameter (AB = 1).
b) - On this diameter AB, there is (AC = 0.78...).
c) - From (C) draw a perpendicular (CD) to AB where (CD) intersect this circle at point (D)
d) - Result: (AD) is the square root of (AC = 0.78).
e) - Inversely, (AC) is the square of length (AD).

End of spatial calculation.

One get the square root and its inverse of any length situated from 0 to 1 using this same theorem.

Some visitors are a little self-sufficient to come here in the Dakhiometry, with his ready-to-wear Mathematics fruitless Pythagore-theorem.

How the Dakhiometry Lamca theorem allows to get simply the following ratios:

              Pi/4 = (a2) / (c2)

Thus, on any any dimension of this following figure, it can verify what is the Universal Space Constant.

Absolute Space Constants This next figure shows how
the LamCa theorem allows to write directly:

Pi/4 = (a2) / (c2) = AD/AH

One can see that the LamCa theorem can perform the calculation of two aeras ratio and inversely.

So what a Pythagore can do in this Impossible Squaring a Circle job?

Sory, but
I am tired to waste my time for translating the Dakhiometry spatial language for the Numbers Religion inconditional and conservative self-absorbed belivers.

The Dakhiometry is not a Religion but the true human rational science

- pregnancy + constant + form + signe (Kuwait)

How to get a circle of a given square (K) perimeter

Fundamental basis

1) - A circle can not be generated from any other spatial form.
2) - While a circle form is the origin of any other spatial form.
3) - Therefore to find the problem of getting an equivalent circle from any other given form, it should be use the basic Space Constant given from a Squaring a Circle properties

- volume + of + a + circle + formula (

Volume of (C1) is equal to the perimeter of square (K).

- given a circle construct the line wich length is equal to a circle perimeter (, Serbia)

Perimeter of (K) = Perimeter of given (C).

Let the Problem of getting a circle with a same perimeter of a given square (K).

Getting a circle from a given square Perimeter It consistes here from any given square (K) perimeter with side (AD), to find how to get a circle (C) with a same one?
To get the solution, it must be associate this (K) to any other squaring a circle spatial structure, for example any circle of diameter (Ax). This structure will give the Constant line direction (AF) that will furnish the solution of this problem.

a) - According to the homothetic property of the universe space, the line (AF) will intersect always the square (K) of side (AD) at point (J).

b) - From point (J) a perpendicular to line (AF) will ALWAYS cut the line (AD) at point (H) on the line of the square (K) side. This is according to that there is always an unique perpendicular from a point (H) to a given line (AF). And more the angle (FAX) is an unique constant of the squaring a circle space structure.

c) - We get then the unique (AH) that is the diameter (AH) of the circle unique solution of the problem.

The solution of such problem is ALWAYS valid whatever any given square side length and any referent squaring direction (AF).
This is the property of the Universal Space Angle composed with line (AF) in this structure.

- This + provided + the + complimentary + squaring + of + a + circle + and + circling + of + a + square (Singapore)

- prove + the + uniqueness + of ++ a + perpendicular + line + drawn + to + a + point + on + a + line (Canada)

- prove + the + existence + and + uniqueness + of + a + perpendicular + drawn + to + a + point + on + a + line (, USA)

If one has some doubt about the perpendicular property then, it may be considered that the line FB is copied at point (J). The JH is a parallel to FB. As FB is perpendicular to AF by construction then JH is also perpendicular at J. JH is then unique because it is from an unique point J, a line parallel to AF.

- square + to + circle + calculator (USA)

This is really a spatial calculator that can calculate both the circles correponding to the aera or the perimeter of any square. It is according to the Transformation Constants of the squaring a circle.

- prove + the + existence + and + uniqueness + of + a + perpendicular + drawn (MARIST.EDU, USA)

Any point (X) on the line (JH) has the same and unique line (JH) as its PERPENDICULAR direction to a given line (AF). It is because any given Angle, for example a perpendicular Angle, is an unique Quantity.

- prove + the + existence + and + uniqueness + of + a + perpendicular + drawn + to + a + point + on + a + line (, USA)

- vodacom + the + process + of + transformation + of + inputs + to + outputs (South Africa)

Probably it concerns this above proof.
The vision of a problem should be realized in a precise view point. For example, considering the Labyritnthe one.
One never can escape from a complex labyrinthe, if being suddenly found standing closed in its center. Why is this impossibility of escaping from such system?

There is is a wellknown popular expression that tells:
"When you have lost your Way the best situation to reconstruct it is to return at the beginning of this way".
Our conscience cannot but construct the precise conscience on the reality of a given object. There is no certainty if there was no defined doubt.
This is to tell that it is at the starting of a construction that one can have a sight on its resolution. It is when one know the Input that one can find the Output.

a) - It is because being in the middle of a system one cannot but see this system as a Whole one where we are belonging to. Therefore, a part of a Whole can never have a sight of this Whole. Being in Internal Side of a system, we never know that it has any External side. That is to tell this Whole has neither entrence nor exit issue if one is a part of this Whole.
b) - But by what means can we escape from a Labyrinthe? It is simple when we have a plan of this labyrinthe site. Does the plan being by itself as a magic one? No, in fact whith a plan of a site, we are in situation of NOT BEING ANY PART OF THIS WHOLE SYSTEM. Therefore, being not a part of this Whole allows us to see this system FROM ITS EXTERNAL SIDE. Thus, being external of a system, the logic allows us to see from its External that there is some Internal side. It is from such logic that with a plan of the site, we can recognize an Input and also an Output relative to this particular labyrinthe system.

In conclusion
The Squaring a Circle, the Trisection of an Angle and other so-called impossible Mathematics problems are due to this wrong concept that the Squaring a Circle and the Trisection of an Angle belong to the mathematicians Realm system itself. It is wrong to belive that it suffice to a Mathematicians to drawn figures and thus, they will a day resolve these problems.

This the wrong internal Mathematics methods that drive to the Impossibility theorem.

How to be abble to positionned for having the capacity of resolving the squaring a Circle? It is as for the Labyrinthe one, to state that the Circle in not INSIDE the mathematicians world. The first thing is to have some solid principle to be abble to state that the Circle is OUTSIDE of the Alive world. To be clear, mathematicians should being abble to state that the Circle Trancends of any form known by the alive. Or practically tell, the Circle is the origin of any of the universe construction. Precisely, it is

The Dakhiometry understanding that there is the Universe Permanence principle from where there is the Beginning of the nowaday universe.

Therefore, with a such problem statement, the man thinking can stay ouside of the Whole universe. One can then construc a logic plan that will show where is the Input and the output of the Squaring a Circle.

This latter problem of the figuring out a circle with a same square perimeter illustrates clearly that the Output solution is found because whe have the Input of it. We are standing in the right logic when looking from the outside of a transcendent system problem. Thus, any problem of the nowaday universe should consider that the Circle will furnishe the basic reasons for. The Circle properties are actually the root of any problem resolution.

Important Note
The Space Constant is strictly the RATIO (AD/AH) of this structure.

The Pi as equal to AD (as the old 3.1416 or the Dalhiometry 3.12019) is only a very particular case for a GIVEN UNIT of the structure.
It is because Quantity in the universe are only expressed in the form of a RATIO of Quantities.

(AD)/(AH) = 3.12019.../4 = 0.780048432857...

This is the basic Constant in ratio form used in the Circle Aera and Perimeter.
It this this ratio value that should be used in place of any old mystic Pi, used in any Mathamtics formula. That is to tell when being rationally coherent, one should use in place of the alone Pi, the basic ratio (Pi/4) expression.

Here above all the formula given in Number are done in Dakhiometry as operations directly in length quantities.

- squaring + the + circle (Malta)

Squaring the Circle is as the sky openning for the rain to fertilize the whole Earth Science Soul Soil.

What is the universe authentic Space Constant?
Beyond the Old/Modern impotence of the false Mathematic Pi !

Squaring the circle perimeter is not an embelishement of the Circle-to-Square transformation. It underline the magic of the universe matter constancy of Quantity.

The dakhi spatial language can define the Space Constancy a:

(AD)/(AH) = 3.12019.../4 = 0.780048432857...

But an another aspect of Quantity can be also be define by its INVERSE quantity. Thus, this above Space Constant can be also used as:

1/(0.780048432857...)= 1.28197168...

However, the Numbers are used here for mathematiciens who can know nothing else than the simplistic artificial pythagorean Numbers.

Only the dakhi spatial language can expressed the universe precision on Quantity. Here after a figure shows how with the spatial language, it can be represented such fantastic Constancy of the univers Quantity. This fact is really beyond the Mathematics impotance that are wholy coagulated under their Number dogma.

- univers + Fleece + tree (Greece)

- pyramiden + diagramme (

the wonderfull Space Constant

This figure represent the squaring a circle structure.

It can be constructed in any figure scale. But to define any spatial structure one should chose any length for the figure length unit.
It is done on this next figure with the square of side length equal to (1) taken as the figure unit.

Now it can be expressed what are the space constancy for Quantity.

Therefore, any length (L2) divided by its corresponding length (L1) is:

(L2)/(L1) = 0.780048432857...

And also:

AH = (L1)/(L2) = 1/(0.780048432857...) = 1.28197168...

Now if this is really a Constant, its inverse value should be equal to the length (AH), under this figure unit system.

The space constant can be verifyed in any construction of figure scale in its both form as indicated above.
If one know the dakhiometry method of space calculation, all these two forms of space constancy can be figure out in their length forms where they are represented with their maxmal universe accuracy that can never be for the artificial Number system.

The usual Mathematics Pi is really irrational with all meaning of this latter word.

- determination + of + the + value + of + pi + when + radius + of + a + circle + is + 3 + cm (India)

This determination when was done in Number format with a usual calculator, gives the value of pi always as:

Pi (numeric) = 3.120493733333333...

When proceeding with any dimension of a circle and the processing was done by a numeric calculator the Pi value is always:

Pi for any radius = 3.12019373...(only this decimal part are chnaged)

However, when the spatial construction is wholy done by construction, it gives always the exact point to point the same Dakhiometry value detrmined in this text. It finally give the length point-to-point representing Pi for any figure dimension. Note that the Dakhiometry can processing with all the four length calculation modes as Add, SUB, MUL and DIV and doing it wholy by constructions.

According to the precision of the Math-processor THERE IS SOMETHING THAT GOES BADLY WITH THE NUMBER CALCULATION METHOD depending to the possibility of the C.A.D. sofware with that one use to draw. These sofwares has no need to produce high Math decimal uses.

- quarter of circle (Canada)

The little circle is exactly inscribed in the main circle quarter. This little circle is also placed at the center of the main circle. And so on,.. there are many other little circle placements. More the little circle is the measurement of doubling the circle and the square fitting with a circle.... In brief, the little circle is the permanent memory of the space structure.

- circle that calculates the value of pi (Philippines)

- animated concentric circles (USA)

- circle + inscribed + in + a + square + structure (Canada)

This the fact. Also in this basic space structure, we can find the secret key of the Constancy of Space that allows precise absolute universal measurements of the universe fullness.

- little circle (UK)

- "erreor" + and + analysis + in + L2 China)

Actually. Thank for your remark and for many other ones.
There was many remarks about this error on L2 analysis. However I haven't understood why there is an error.

May be the error comes from a step of proof that is not detailed explicitly. I am going to put right in the following.

- proof of pi (nextgentel, Norway)

- Descartes proof of impossiblity of construction of doubling a cube (New York, USA)

- formulae (Russian Federation)

- construction science formula figures (Fidji)

- old science theory calculation (Malaysia, 051302Modern_Science_3.jpg)

- John Northern Arizona construction science (, Arizona, USA)

- draw a diagram of how psychology envolved into a science (Philippines)

- pi + get + real + geometrik (Greece)

This next figure is only possible AFTER the result of squaring a circle for calculation of L1, L2 and L3 by numeral process.

The Algebraic method is in numeral incapacity to access to the space structure.

The uniqueness of the squaring a circle is a space structure that need to be resolved ONLY by the Dakhiometry spatial construction method.

Formula Determination for Pi Consider this next added figure.
When we have seen above that
L1 = [c.(sqr(2)]/2
it is clear that according to that L1 is the half diagonal of the square circonscribed to C, the little circle (C''1) of radius equal to L2 is equal to:

R(c''1) = L2 = (1/2)[c(sqr(2)-1)].

Thus the circle C'1 diameter on figure-4 is :

Diameter of (C'1) = 2 times L2

Because of the C' radius are double of the C one. Therefore, to compare radius of C1 to the C'1 one is equivalent to compare C1 radius to L2.

Thus, there is no error of proof. Only a step of proof not explicitely exposed.

Examine this next figure. You will see unfold the rich consequences of the circle/square structure. For example, the inscribed square in the C circle, of side L1, is equal to the quarter of the C' one.
It is not as the old usual mathematics that institutes receipts in huge works like any Civil Code. Then this latter is used to format the human brain. Therefore, Mathematic are not laws but consequences of empirical tricks compiled along the time. While the Dakhiometry knowledge method is to practise reason deduction from most fondamental but simple real laws to construct the complexities of the universe matter.

In brief:
* Or one should renounces the Dakhiometry and do not try to integrate it into the old Mathematics,
* Or with an open minded one can get into the real new way of knowledge to be abble to construct the wealthy life for everyone and for all.

demonstration of C1=C'1 is given hereafter.

- numerical value of pi (Australia Univ of Queensland)

- graph of pi converging series (Canada, Ontario London Ody)

- circle pi 3.12 (USA)

- Transmutation circle no background (Singapore,

- unprecision calculation (, Belgrade, Yougoslavia)

- nows + of + Cambodia (Cambodia)

Determination of Pi

A homothetic of k=2, with center O, give C12 = 2.C1. Lengths are only considered. Thus C12 contains two C1.

The same homothetic transformation place point O1 at O2. Then, we have OO2=2.OO1. Therefore the two red circles are equate. That is : C1 = C'1.

In consequence, the center of C1 is O1 and is also on the intersect of C' and a diagonal of the square. Remind that C1 is the little circle inscribed in a quadrant of C.

Introduce the square circumscribed to the great circle of diameter [c]. Drawn a quadrant of radius [c]. The little circle C'1 has a diameter [d] equate to :

d = c (sqr(2) - 1)

With a homothetic of center O and a literal constant of 2, we can see that the circles C'1 and C have a same radius. Therefore, C'1 is equate to C1.

From figure-4 we get the value of the radius of the circle C1 as :

radius of C1 = (1/2).(c).((sqr(2) - 1)

With this latter relation the red triangle of figure-1 is completely determined as functions of a, b and c.

L1 = (1/2).(c).(sqr(2))

L2 = (1/2).(c).((sqr(2) - 1)

L3 = (1/2).(a + b)

The determination of data for a precise Pi value using the compass and the rule is completed.

Note that along these analysis for the determination of the universal constant, we are reading only spatial structure represented by different figures. Also, figure are spatial matter even if they are done in coarse manners their logic remain in our mind. Nothing of artificial or arbitrary determination was introduced. Therefore, the value of this Constant is an authentic positive fact and belongs really to the Permanence of the matter space.

- pi + value + calculation (Bangladesh)

Now we are going to finish it with calculations. Obviously the red triangle of figure-1 is a rectangular one. Therefore Pythagoras' theorem allows to write :

L22 + L23 = L21

Hereafter are developments of successive calculations of the Pi value :

Determination de Pi
Determination of Pi
Determination of Pi
Determination of Pi
Determination of Pi
Determination of Pi
Determination of Pi
Determination of Pi
Determination of Pi
Determination of Pi

- Transmutation + Circle + Philosopher + S + Stone (

- squaring a foundation (, Ireland)

- squaring a foundation (, New Jersey, USA)

It is true according to that squaring a circle allows the just understanding of circle from there can proceed fertile deductions.

- real + value + of + pi (India)

The constant Pi is a ratio of surfaces as :

Determination of Pi

- true + value (USA)

There is a basic spatial proof of the squaring a circle, doing according to this ratio. The circle and the square surface externally tangent to it, is a constant immutable ratio that one can determine for this proof.

- quantum circles (, Oklahoma, USA)

- what is the value of pie in maths friction (Pakistan)

- is + there + a + pattern + in + Pi

- pi + accuracy

We get finally
the new natural constant of Pi and also some of its characteristics, as follows :

This formula writen under algebraic Form
can be caluclated directly according to this form, by Spatial Construction.
This gives precisely the corresponding LENGTH-of-Pi Corresponding to the given figure unit !

It is very useful for CAD softwhares.

Remind that this algebraic Formula is originally the result of Spatial Construction.

Determination of Pi


- the + whole + pi + equation (Canada)

- value of pi Romania

- ""

- formulas + Pi + for + kids (UK)

- simple + equation + to + get + pi (

- new + value + of + calculating + pi (India)

- new + method + of + calculating + pi (India)

This next above Pi under numeral formula can be purely with length constructed as shown next in this present text. And if a Length is considered as rational mathematic element then, Pi is necessary perfectly Rational. - the + numberto + of +pi (, California, USA)

"what + is + the + mathematical + value +of +Pi ?"

The practical values of Pi may be as follow :

1) - Accuracy of 1/1000 : Pi =   3 . 12

2) - Accuracy of 1/10 000 : Pi =   3 . 12 02
3) - Calculator accuracy :
------- Pi = 3.12 01 93 73 14 31 77 5 ....

Therefore, the most current friendly-use of Pi, in human scale is the first choice.

It is to say e.g. : "Free Point Free in Free" numbers.

Also in my mother tongue : "Ba phêt Ba Ba" Sô.

For all the other languages, forgive me please, it is only because of my ignorance that stops me from chat.

Your notes:

- practical + notes + on + determination + of + the + value + of + pi (Ghana)

- "02 + pi + numbers"
- ...

- what + are + the + 2 + lowest + integers + which + when + divided + produce + the + result + of + pi (USA)

So you have find a such simple integer formula.
For me, I get it simply with the help of a computer. For the common Pi value of 1/1000 accuracy it is :

( 234/75 ) =  3 . 12

It seems to be easier to write directly the numeral 3.12

Hereafter, when c = 1 unit. The unit is understood as 1 miles, 1 km, 1 a.u., 1 micron,... and not 1 length quantum, because at quantum scale, there is not square and Pythagoras' theorem!
Thus, when c = 1 unit, (a) and (b) have particular values as :

Determination of Pi

Practical uses of circle and square equality :

The perimeter of the circle

- formula + perimeter + of + a + circle (Albania)

No change is for the formula concerning circle. Therefore :

perimeter = 2.Pi.R
With R the circle radius and Pi the above value.

The circle perimeter definition
The circle perimeter Until now, it was impossible to measures precisely a circle perimeter. For the dakhiometry, the reasons is a fundamental property of the matter. Geometry was built on the continuity concept of the world and it was founded on the Continuum of a Line. Despite a point was an intersection of two lines, this definition is untrue even if one is not conscious of this contradiction. From a view of a World described with Lines, impossibility appears because of the contradiction between the Continuum and the necessarily definition of a Point. All Geometric figures are only construction of Lines. This is for the circle that appears as a Line, the famous perimeter.

Therefore, knowing a circle is knowing how to measure its perimeter. This perimeter that is a useful measure for the daily practice, however this measure was until now an impossibility. And it is ignored that the fundamental reason is the great contradiction between Continuum and the practice of reality. Precisely this reality is no more than the Discreet Matter. On this figure, in the case of figure a), one try to do what is possible in practice that consists of measuring the circle when it rolls on a Line. This problem was a so great mystery that on can find any thing as a result. For example, it was found that using a process of one-to-one point correspondence, one can prove that the infinite blue Line, is equate to the half of the circle perimeter. Another thing is to try to paste a polygon on the circle, until it may be confused with the circle perimeter. Any operation is impossible according to this knowledge of continuum base. This is because a continuous line can not be "broken" into dinstinct points.

On the lower figure b), it is represented the same circle rolling on a road. Now, we are in the thought of the discreet Matter. One can now applied the one-to-one process of point to point correspondence. Therefore, the perimeter that is composed of the out most exterior quantum of matter of the circle surface. It can be now counted in point to point correspondence with the straight blue "line".

We can say about the perimeter of a circle that it is a current useful practical measure, e.g. when one want to know the length of a thread of a spool of cotton or the distance of a running car.

Remind that a circle perimeter exists really and is formed by a series of discreet matter elements.

- "discribe" + the + closed + loop + system (UK)

- what + figure + is + formed + by + the + intersections + of + two + planes

Sorry, no figure is formed by two intersecting planes.
It is only imaginary figure that one uses for the belief of a LINE. This latter is the Euclide's definition one. With a line, one must go as far as a line drives him in straight line. And there one have to define the Infinity for validing the line. Inversely the Infinity generate and valids the Line imaginary. Therefore, in closed loop one remains shut up in the Nothingness of unfounded mathematics.

What is the intersection of two planes ? Only a direction. And a direction is not a line. A clear realistic example is shown in technology. It is the rudder, the elevator, the planes of airplane and also of an arrow. These rudders are planes for directions. Then, two plane are efficiently used for direction controls in that, the arrow body is not a line but a finite segment.

A line is a human obviousness preconception that give raise to a false concept. How to distinguish what is the true ? Well, mathematics generated from Line concept are limited while mathematics founded on circle are rich and fertile. You have there a great example : the squaring a circle that are never understood by the traditional mathematics buitt on Euclidean's Line. Would you like to have a long listing of great mathematicians that fail on this attempt ?

The Continuity of a Line is a contradiction

The Continuity comes from Euclide's postulates defining a Line of the Geometry:

1) - By two points there is always a unique line.
2) - A Line is unlimited.

What were resumed by David Hilbert who wanted to a pure abstracted Geometry.

3) - There exists at least a line passing at two given points.
4) - There exists a maximum of one line passing by two given points.

Hereafter is how the Continuity meets its contradiction because the Continuity generates itself a Discontinuity solution.

- play + full + "pastulate" (Pakistan)

- theorems + and + "pastulates" + in + geometry (India)

- geometric contradiction (Korea, WPro/images/blog_4/art_3.jpg)

Geometry is a whole contradictory method because it rests on the Euclide's definion of a Line. This definition has no consistency. when it rest only a simplistic "edge of an infinite ribon" existing in a Continuum. Therefore the Goemetry and all the Mathematics don't know what is a true Line of the Linear realm.

The continuity Contradiction

Let a right triangle ABC inscribed in a circle. On this figure 4-3, one can think that the circle circumscribed to ABC is the entire locus of the vertex A. But it is not the true when A is at B or at C. The above pastulates postulats and axioms indicate that no longer there is a right triangle when A is on B or on C. The common obviousness does not be surprised, because this conclusion seems obvious when there are no longer a three vertex triangle. But this evident acceptance masks a serious contradiction.

- theorems + and + "pastulates" + in + geometry (India)

- "pastulates" + of + quantum + theory (Pakistan)

The aim of a theory is to valid pastulate into postulate...

- geometry + pastulate (Philippines)

- Pastulate + and + Theorem + in + Geometry (Japan)

I see... Very famous mathematic Pastulates...

- "pastulate" + theory (Australia)

- Discrete + Math + Prove + that + "teh" + product + of + two + irrational + numbers + is + always + irrational (Canada)

For more accurate analysis of the situation, introduce the center of gravity G of the triangle. The center of gravity is a fact of "the object triangle", as well as for any matter object. Thus, when the vertex A varies, the center of gravity G varies also. Properties of a center of gravity of a triangle are known. Therefore, the locus of G is a circle centered at O and with the diameter equal to BC/3.

If this circle is entirely détermined as the locus of G then the right triangle is also entirely determined at any position in its circumscribed circle. Otherwise, there are undefined cases.

Thus, when the vertex A is at point B or C, according to postulates and axioms of Euclide and Hilbert, between B and C there is only one line. Therefore, the three medians disappear and also the center G. Between BC there is one line and no more right triangle. A discontinuity exists in the locus of G and also in the locus of the vertex A.

In conclusion, the above Euclide's postulats and the Hilbert's axioms imply that the diameter of a circle is always a discontinuity where the right triangle is not defined. We get there an astonishing result where a Continuum can be used to prove the Reality of the Discontinuity. Unhappily, this is only a contradiction of the Continuum concept.

- compilation of all geometric theorems and postulates (?)

There is an interesting result from this indefined triangle when point (A) is at (B) and (C) positions.
Because in such situation, there is no triangle with the sum of all its angles equal to Zero degree. There we have:
The Angle (A) is an inexistent summit (A).

Therefore, it gives rise to a fundamental result concerning the statement of the Pythagoras' theorem.
If it is the current statement that the Pythagoras's theorem is concerning a rectangular triangle inscribed in a circle then, this Pythagoras's triangle is not valid when the triangle is reduced at the circle diameter. Thus the rectangular triangle in a circle is irrelevent for the Pythagoras' theorem.
While with the Dakhiometry's definition according to the Lam-Ca theorem, it is used here not as rectangular triangle but only aeras are concerned as its basic statement.

Consequently the surfaces:
BC2 = BA2 + AC2

According to the Dakhiometry Lam-Ca theorem this formula is always valid as aera summation equalitties. The Lam-Ca secret is the use of aera and not with only linear segment as is done in Mathematics. Because Aeras can be attached to circular properties.

It is why the Dakhiometry Lam-Ca theorem rests on more basic foundation and is quite different from what is denoted as the coagulated Pythagoras' theorem statement

The idea of the Infinite and the concept of the Unbounded

The Infinite concept is impossible to define. And this concerns also for the Non-Being and the Zero concepts. Until now, the human thought seems to please to refer there. The proof is that these thinks lean on a certain Continuum, or the Infinity.

Here are therefore contradictions engraving these notions.

One "thinks" Continuum and Infinity in manner so uncertain that one has the pain to take conscience that these thoughts are not possible without the Discontinuous of the matter. There are therefore giant theories, that build the Continuum with the Discontinuous Facts. If one asserted that everything is taken shape drowned in the Continuous, one however ignores that this Continuous non-distinguished world is necessarily constructed according from brick to brick process. Because, what is a Cut in the Continuum of Real numbers? Why can one distinguishes "holes" in rational numbers, while this world was supposed to be a Continuous? If the Whole natural numbers appears in First, how can one assert that the World is a Continuum?

Here is a precise example in mathematics, for defining the Infinity. Note that the Infinity is a consequence of the Continuum and that Zeno found this world too narrow, without possibility of movement.

One defines that the Infinite number is a number that is larger than any given number.

Fatal contradictions:

1) - As stated, the Infinity is not a number, because, "larger than" is not a quantity neither a uniqueness.

2) - this definition of the Infinity leans only on the Discontinuous of the World, because,

- "any given number" is a property of the Discontinuous World. And if there is one Discontinuous reality then, this Continuous world is a contradiction,
- if, one could propose a number "larger than", this means that this number would not be Infinite. Result: this definition is only a proof of the Discontinuous and, ever, one reaches the Infinity that this definition seeks to define.
Aah! If Zeno was there, he would tell you his history of a tortoise that runs faster than the wind...

In summary:
One finds thus, in education works the erroneous and uncertain notion : "The infinity is a number larger than any given number".
The error is hidden under a seemingly formalism. This last masks the unavoidable uncertainty of the Infinity notion, the philosophical or mathematics ones, because precisely, it comes from its absence of conscience in the human thought.

The natural just concept is the Succession that generate unbounded and the Without-Limit notions. Thus, the real definition should be : "The Evolution of the Life is such that, to any step of the life, there is always a one by which, Life can go further"
This is not a theorem to prove. One can only verify it, because the Succession is a Fact of the matter Movement, called the Recurrence. According to this unbounded evolution, on can say that the Uniqueness is a characteristic of the universe. The old mathematic known series are very poor system due to language of number that drive to traps, holes, forbidden things the most strange.

Conclusion :

This is an exact definition of the Without-limit of the Succession Fact of the natural number series.

One can then state: The Without-Limit is represented by a series of numbers the succession of which can exceed any given number.

The series of Natural Numbers is a such series, that represents the Without-Limit, or the Liberty, of the Evolution of the universe.

the notion of Without-Limit can be understood as next. We suppose to be standing on an immense plateaus of earth. Walking on this terrain, step by step, represents the discontinuous of numbers. Then, we tell that this terrain has a limit, if in the course of our step, the ground gives way, because a ravine delimits the terrain. Another case, is that this immense plateaus, has no Limit. Then, one would tell that to any number of steps that one can make, there is always this one that one can do more further... It is thus, the notion of the Without-Limit the same as the one of the Absolute Liberty. It is now a problem for everyone of the human. On the place of the Infinite word, anyone has to invent again, the just term expressing this real Withiut Without-Limit notion that one finds in the natural numbers series properties.

- what + were + the + first + machines + that + could + process + equation + "withiut" + human + direction (USA)

What are the view points of the Dakhiometry about this problem ?
For the Dakhiometry, matter is discret and the quantum space is obsolutly defined. Lines are only directions determined by the motion in the recurrent process. That is to say lines and precisely segments of line, are only regularly succesive quantum locations in a precise direction.

Therefore, lines and segments, are composed of a series of discreet matter. In brief, lines and segments of line are matter.

Resume the above representation of a right triangle ABC but it wil be defined in the view point of discete matter.

The discreet matter

Let be the intersection of the medians of the right triangle that gives the point G. This medians are matter and can not appear or disappear without doing it according to the matter conservation laws.

Thus, when the vertex A is at point B or point C, the medians are always matter reality. They are in these positions, aligned to BC as shown on the figure 4-3, according to matter characteristics. One can see that these three segments of matter can yet define a center of gravity G. This means that in the situation where the vertex A is at B or C, the median lines of matter are not vanished and confused. They can again represent a center of gravity of a particular right triangle form.

There is no position where the right triangle is undefined as for the continuum of the Geometry.

Practical Notes :
To see if G is at the center of gravity, one can divide each medians into 1/3 parts. Then, one can count these parts at each side of point G. The result must be the equality of matter between the two side of G. on this figure, one can see that on the side GC, there is six parts and on the side AG, there is also six parts. This means that G is the center of gravity of matter shared along BC.

Conclusion on the Continuity of the Line in Geometry

For the Dakhiometry, the circle circumscribed to a right triangle ABC is entirely defined as the locus of the vertex A. While for the Geometry, there is a Discontinuity in this locus and the triangle ABC is not defined when there is only the hypotenuse. This is not due to logic relationship but only a great contradiction in the principe. Because, the Discontinuity defined by the Continuity is a fundamental contradiction. They are two contradictory concepts, the one is True and the other is Untrue. One can prove that the Continuum is Untrue.

Therefore, it is a fact that the Continuity postulates and axioms of the Geometry generate Contradictions.

Some remarks and questions visiting this Evolution site.

- would + the + value + of + pi ++ be + the + same + if + a + larger + weight + had + been + used

The value of space is not dependent of mass of matter. Space value are concerning location and distance.
Because from the Anciant's time, space is nothingness. Thus any Geometric value is not depedent to mass.
In Dakhiometry, space is concrete matter and length is a matter, thus the question of Pi value according to mass is a valid one. However, foundation of space matter rests on the existence of elemental immutable matter. And this state has the property of without-interaction because being immutable the elemental matter don't obey to interaction laws and has no weight or mass. Thus element of space as points and lines are pure distances absolutely located. Therefore, a length value is an absolute one and do not depend of any another physical factor else than as exclusively with absolute locations.

The Pi value that is a space constant, is only disatnce of absolute locations.

- value + of + pi + prove + cut + the + circle + rectangle (India)

- In + triangle + ABC, + lines + are + drawn + from + the + vertices + to + the + first + trisection

OK. In continuation, from the other vertices, draw trisection of each... then you get the Morley theorem figure. There is a means of doing trisection in similar way. The Morley theorem is proved simply in Dakhiometry by trisection and this Morley's figure is in fact a consequence of the trisection process. It is the same for the Achimedes' figure of trisecrion, with circles that are only consequence coming after the trisection construction.

- everything + in + Geometry + is + built + out + of + point

This is a fact of Geometry, because its foundations rest on the Continuum. In Dakhiometry, points are absolute locations of space. Also figures are precisely located at these points. But points are only the two ends of an ultimate elemental length. From that, it is a property of space to be named precisely by natural number series provide that this series can be adjusted to the scale of lenghts. Example for 1, 2, 3,... It may be km, cm, picometer, or elemental sacale scaled unit.

One see that with Geometric points, the Anciants cannot use Geometry for calculation with numbers. The modern Real number series is example of tempting to name the Continuum but unsuccesfully because of Principle contradiction in that Continuum Conrinuum cannot be Discretness of a Name. From there, Numbers begun to be buit as a dichotomic part detached from Geometry.

- GIANT + "CONRINUUM" + 7 + instructionq (Hong Kong)


- pi + + false + proof + -Bible

- how + was + pi + named + in + the + Bible ?

- is + true + a + circle + is + determined + if + a + given + segment + is + its + diameter

Is true.
The basic proof is as follows.
1) - The Symmetry is a basic property of any object in the universe. Thus, the object center is a given data to define this object.
2) - A circle is defined by it given center plus one point of its circumfrence.

Now, a GIVEN segment is defined by its given center and its two ends. Therefore, necessarry, a given segment is sufficient to wholy define a unique circle, as long as they have the same center.

It is why a circle has one unique diameter length.

Atchimedes' Centre of Gravity.

Proofs of solid aeras and volumes are FALSE. With his gravity center he did succeed to prove the validity of solid measurement.

Please Click here :

Archimdes' gravity center method is invalidated.

The Geometric construction
of a straight length equal to the Pi value

- "discover + of + the + circle + circumfernece"

Hereafter is the Geometric construction of a straight length that is equate to the Pi value. That is to say, the Geometric straightening of the curvature of a circle circumference is a reality. Therefore, a circle perimeter can be obtained precisely as a straight segment..

Now that the Lam-Ca theorem is more familiar, it can be presented here, another way of squaring a circle and a method of constructing a straight segment equate to the perimeter of a circle.

Theorem of the straightening of a circle perimeter

- galileo man square circle (, Hennepin Medical Center, Mineapolis, Minnesota; USA)

- "cicle" + surface (Japan)

- how + can + I + prove + that + the + "area" + of + a + circle + is + pi + r + squared

- maths area coming off a circle (, UK)

This is the truth.

- super linear transformation (, Provider of SaaS Web Security, USA)

- morphing a square into a circle (Bangladesh)

- circular cutting apparatus (Turkey)

This next figure shows that one tries to tell what is a circular aera by means of linear realm tool as the rectangle.
However, only a circle can tell what is its true aera. For this purpose, we can tell what is a circular aera when we get the Key of transformation from Circular realm into the Linear one.

- finding the perimeter ":od" a difficult figure (Philippines)

Surfaces as proportional to length

The circle surface appears as rectangular or square surface. Then, it is why the proportional constant denoted as Pi is a problem since a long time. The figure show to method of how to define this constant as a factor.

- Transform a rotation into a linear back-and-forth movement with simple harmonic motion. (Virtnam)

Question for those who believe to their irrationality of Pi demonstrations.

- algebraic + proof + irrationality + of + pi (USA California Santa Cruz Univ.)

Any algebraic proof of irrationality is done according to the mathematic convergence methods and to successive Euclidean divisions. These types of methods are necessarily the unbounded accesses methods denoted as irrationallity. Therefore, the irrationality is not concerning a numbers characteristic but only the irrationality of bad mathematic's methods. A bad method is only a false method and can never be classified as a mathematic irrationality discovering.

- formulas + N + "which" + pi + appears + in (USA)

Actually, we have the natural Integer numbers series that is written as :
N = Pi.x
as shows in the following where N=circumferences and x=diameters.

- irrational habit plane (Shiraz University, Iran)

The proof of circle surface (S) in the following uses summation of circle perimeters or circumferences (P) that compose it. Then, one get (P) versus diameter (D) :
P = Pi.D
This perimeter is then a linear function of the diameters.
Products of irrationnality produce the natural integer an irrational numbers. Consequently, any circle perimeter is function of diameters varying from zero to any number of the universe. Then, this perimeter (P) can vary from zero to any number of the universe. Particularly all these (P) numbers necessary contains the natural Integer series beginning from 1 to unbounded great quantities. The figure here, shows the graph of this linear function.

Thus, why a product of the irrational Pi give raise to the natural integer number series ?

Every provers of the irrationnality of Pi, have to make a point of giving an answer about a such FACT : why irrationality produces rationality ?

- irrational + numbers (Niger)

Here is only a particular exemple. There is a basic proof that irrational numbers are contradictions. Because it can be proved that any Natural Number is irrational with an exhaustion method. And inversely, we can prove with compass and edge that any number, include the whole Natural series ones, that all quantities can be precisely and exactly determined.

Theorem on integral calculus for a circle aera

- PI + "MATEMATICS" (Slovenia)

... a new most simple but exact method. - mathématics + integral + concepts + and + formule (Mexico)

- how + many + degres + has + a + circle (Canada)
AAny given value is valid as representing a circular cycle. Therefore, one (1) is valid and any natural integer number is valid. It is why the space constant (pi/4) is rational because an operation on an irrational number is known as producing irrational result. This prove also that irrational mathematics are the most confude and contradictory formalism.

- why + are + circle + graphs + mostly + "alway" + named + circle + O ? (USA)

... HELP !!!

- physic + and + technologies + invention + 2002 (Phillipines)

- the + universe + observes + itself (USA)

Because matter is memory and the thinking is constructing reason on memory data the universe seems observing itself. However, this matter process is not a closed loop system. A closed loop produces bounded process from there one can say that the universe is an observed observer. While building New reasons from memory is a Succession process. Because this latter is a Recurrent one, the alive universe is unbounded existence based on a finite quantity of matter. From there it appears as Matter Conservation principle conserbation. Therefore, the universe of the alive is an open logic system based on permanent foundation.

- law + of + "conserbation" definition (Canada)

Finger motions is not an uniform one... this the last experimental statement.

- pi + value (Hungary)

- proof + that + pi + is + transcendent (Israel)

- determination+of+the+value+of+pi (Ghana)

- counted + pi + value (Finland)

- taoism + and + concentric + circles (USA)

- the+universe + observes + itself (USA)

- What + methods + have + been + used + to + find + a n + accurate + value + for + pi (Montserrat)

- finding + pi + by + rolling + measuring + a + circle

- basics + construction + fondations (Canada)

circles and curvatures are internal properties of circular structure. Any measurements of circles through linear function must necessary uses the Constant factor of spatial circle transformation. In the following, is a theorem on circular aera integral calculus measurements using circumference in discrete matter :

- what + is + Circularity + maths + and + science (Zambia)

- pi + value (Maldive)

- parallel + world + equations + the + proof + that + "ther" + is (Australia)

- why + circle + of + life + and + not + a + square (South Africa)

- quantity + of + cars (China)

- transformation + from + square + to + circle (USA)


- mécanique + propriété + matière (Vietnam)

- mathematic + formula + to + calculate + circle + lenght (Latvia)

- the + meaning + of + the + "ying" + and + the + yang (Ivory Coast)

Actually, beginning of life was born from two matter structures that contribute all along the universe history to furnish basic materials and reasons developments for construction. As a Mother and a Father are two complementary structures linked together to be able to prepare a child, they are characterized as the yin and yang principle of life. The two necessary circle and squarre structures with which an unbounded way was opened. The Yin and Yang are not ideology but only observations of the reality of the universal life possibilities extending on heavenly globe bodies that fit to physic conditions.

- square + and + round + archetypes (USA)


- spatial figures (Philippines)

You are right to underline such notation.
Denoting of "spatial figures" is specific to the Dakhiometry language to define spatial constructions of figures using basic elements of space as point, line and curve.
Obviously one use to tell that it is Geometry. However, it should be distinguishe the Dakhiometry from the old Geometry. Even if the forms seems to be the same but the mode of thinking is quite different because the spatial language rests on true principes of the universe's concrete and discrete absolute space. In fact Geometry is only figure formalism abstraction and ignores what is the universe space. For Geometry, the space is rather the inheritance of the Anciant Nothingness ideology. It is why Geometry was early a dead-language and was overcome by Algebra and Anlaytic Geometry methods that use Number formalism jointly to graphics. These latter are not spatial constructions but resulting from numeric algoritthms.
The spatial language is unbounded in fertil manners. For example calculation are done by simple easy and fast construction using space elements. It is done in precision and exactness if point location without suffering errors from neither irrational Number holes nor infinity limits of "not-a-number" methods.

- Day length as a function of latitude (USA, Mary Land)

- constructing spatial figures (Philippines)

- varying length of day and night (Philippines)

- how to calculate the sinusoidal graph for day duration for Melbourne (Australia)

Actually, concerning Melbourne, all the Earth seasons are the reversed ones as shown on this next figure. The day duration with a good approximation, may be considered with the Earth considered as a perfect sphere. It is because on any Earth latitude, the day cycle is the same.


Day lengths Length of days along the Earth ecliptic can be defined by spatial figure as the next one.
On this figure, the North altitude is shown from 0 to 90 degrees. Length of days are defined by different latitude circle perimeters. All these circle denote 24H time of a day. They are face to the Sun normal view toward the Earth but on this figure is represented what does the Sun see on different Earth globe latitudes. The red part of any circle are durations of a days according to its latitude and the reminder of its perimeter in blue color denotes the Night duration.
This figure represents the Winter and Summer Earth solstices for the North hemispher. For the South one, we have to permute the color of the perimeter as night for day duration and inversely.

Fot the equinox in Spring and Autumn the Earth pole axis is in a plane perpendicular to the Sun radius. This produce an equi-axis Earth distance from the Sun. Therefore, the 24H circle duration is divided in two equal parts for the day and night perimeter lengths.

- convert a circle to a rectangle (USA nih gov)

- squaring + the + circle + equation (UK)

- squaring + the + circle (Belarus)

- impossible algebra formula (USA New Jersey)

- four bugs simultaneously crawling towards each other, square, physics (USA NMT edu)

- Sacred number formula revealed

- description of E.T.'s over time (USA)

- sacred physics (King Country Library System, USA)

- circle pi circumference (, USA)

- optimal disposition of squares (Canada)

- proof + squaring + a + circle (The University of Texas at Austin, USA)

- proof with mathematical pi (

- the root of all action square root of two (, Toronto, Canada)

You have get an insight of action practice. So, plough more further to gather in the crops.

- nuumber pi figure (, Missouri, USA)


Pi length
Resume to this figure:

Let SAD the greater square surface of side [AD] et SAB the one of the little square of side [AB]. The ratio of these surfaces can be written as :
SAB/SAD = Pi/4

This a form of the Space Constant given from the Squaring a circle. It will be very usefull in the following.


       y = (------------------>)

- The circle perimeter formula.

The universe Existence is as a toggle of light. But at the beginning light was not a phenomenon. The universe beginning is rather a toggle of knowledge owing to the starting possibility of transformation of curvature into straignt straight line. We human can know this universe event using the space structure logic. Then performing a squaring the circle we can get the process of how space use to go from a curve into a staright line. The square was a new space structure born from the circular one where measurment can proceed for the beginning of the universe construction.

We have seen that the squaring a circle is done using a space Constant. Then we can know how to transform any circular line into a straight one and inversely.

This transformation also must be refered to the basics space structure where the universe is originated. It is the circle and the square associated structure. This latter is a circle inscribed in a square or inverseley a circle circonscribed to a square. This two forms are related between them by the space Constant. Therefore, we can write the immutable relation between the perimeter of a square and the circumference. If (D) is the side of the square and the circle diameter; (P) the perimeter of the square; and (C) the circumference, we have :
P = 4.D
C = P . pi/4
P = C . 4/pi

The space Constant is used here as (pi/4) or its inverse (4/pi).

According to these relationships, the circumference formula is given as :

C = pi.D It corresponds to,

C = P.(pi/4)

- fundamental + theorem + proof + different + equation (Vietnam)

Dakhiometry theorem

1) - Theorem of the circle perimeter
The perimeter of a circle is equal to the perimeter of the square of side the circle diameter, time the space Constant (pi/4).

2) - Theorem of the square perimeter
The perimeter of a square is equal to the perimeter of the circle of diameter equal to the square one, time the inverse space Constant (4/pi).

- Reciprocal + formula + for + construction (Hongkong)

- when + was + the + first + circle + invented? (Former Czecholovakia)

- formula + for + finding + the + perimeter + of + a + square + when + you + know + the + "diaginal" (USA)

- circle + perimeter + formula (Singapore)

Bows practical application

Bow lenght
The space Constant is then means of figure out any circular bow lengths. Inversely any straight length can be define a bow length legth in a any circle. This can be done in any dimension dimansion. These applications should use the corresponding suqare square-cercle structure. Example is show in this next figure in that there are drawn two equal circle bows and their corresponding half square straigth lengths. In theses structures an angle define a proportion of the bow and it equivalent same proportion of length, in the square perimeter. Basic square-circle structure are square and circle inscribed or circonscribed. From these equivalent, one can extend this equivalence to any dimension according to proportion defined.

- "legth" + circular + loop (USA)

- finding + "suqare" + root + algebraically (India)

- tiny + pi + calculation (Italia)

- bow + distribution + exercices (USA)

- surface + "area cylindar" (USA)

Why the empirical process of convergence
by exhaustion like the polygon one,
is an error erreor when founded as an axiom

- manipulate + nothingness (Germany)

A fine meaning in words association.

- trancendent + classes (Mexico)

- define + Tchuan (Canada)

- polygone + inscrit + et + circonscrit (Canada)

We have now the mean of the transformation process between straight line and curves. It allows to understand why the Archimedes' exhaustion can't be a success and why with modern calculation machines polygon exhaustion can't get the excat Pi value.
The polygon axhaustion method is a very fine idea and eveyone of the best may end to use this polygon method because it seems the most efficient.

One don't have to mask this event and reminds that no mathematicians from Archimedes to all the modern ones, nobody never being able underline some controversial point about the old pi value. The Squaring a circle was forbiden as impossible problem and also as heretic subject. The more, since during four years, my publication on this site about the squaring a circle meet silence from any scientific institution over the world. This last fact is a real aberrant heretic occurence that is a real odd thing today. So, for all institutional matheamticians, I hope you will fully take advantage and make the most opportunity of the Squaring a circle fertilities an also to avoid so many errors generated from the current methods.

This is only a particular point of the Dakhiometry. This latter opens up more larger new horizon that mathematics can't never predict.

- pi + structure (Cocos Island)

It is the just concept : a space structure constant. There is large consequences that simplify the space knowledge.

- answers + for + "Archemides" + problems + in + high + school (Germany)

- Archemides + organization + in + estonia (, North Estonia Medical Centre, Regionaal haigla, Estonia)

- define + physical + factors (Jamaica)

- squaring + or + "squarring" (USA)

- ultimate value of PI (USA)

- algebraically + prove + that + a + circle + has + a + larger + "area" + than + a + polygon (UK)

- how + many + segments ++ will + fit + on + "teh" + circumference + of + this + circle (USA)
There is no number of linear segments that can correspond one-to-one to a circonference, even if we can count the immutable elemental matters. Because linear and curvilinear lines are of two quite different logic worlds. When operating in the linear world, and try to resolved circle as a polygone constituted by points as sides, comes from ignorance of this basic space difference. The only means of comparing these two worlds is not to directely linked them point by point, but to leave the one and enter into the othern by means of the Space Constant.
Ignoring the Space Constant, drives Galileo to prove that an infinite line correspond one-to-one with a half-cirle length. This is the infinitesimal Continuum world where every thing can be confused and allows to produce many dogma.


- discovering + pi + as + the + limit + of + perimeters + of + polygons (Canada)

Convergence and Exhaustion methods errors.
Ignorance of matter space

- draw square with compass (USA, Texas, Abilene McMurry University)

- périmètre + polygone + exinscrit + supérieur + cercle (France, Lyc-Curie-Sète Ac-Montpellier)

The 1er space postulate

- a + circle + may + be +++ drown ++ a + point + as + center + and + any ++ length + as ++ radius ++ is ++ this +++ stetment +++ postulate ++ or +++ theorem (Eritrea)

This a most important questionning about our conscience on what is the Being of universe Facts. This precise root determination from where reason of everything can rest on immutable basic reality. Root from where our conscience can be built to be in concordence with realities.
The root of reality as source of truth beyond which there is no more though and from there unfolds any reason of thinking. Each of human should recognize and meet there such universal Facts because aside imaginary any human can't but rest on such base.
From any root reason there is always down stream reasons of thinking and never in upstream direction where there is a blankness effect.
According to this basic characteristic, we can define such root reason as Postulate when no more possibility can be meet to find some more upstream one. Then, as source is always going downstream we can define what are consequences deduced from root reason as a Theorem.

Concerning the circle, a point as center for two points of a compass is equivalent to a circle as a constant radius from a point. These two propositions are equivalent and both can be valid. Therefore, these reasons are not an unique reason. They are not the uniqueness of a Postulate because from a point as center or an end of radius we can produce unlimite particular circles.
Thus, a circle postulate should give the uniqueness of a circle concept. We have to note that the space has two characteristics. Space is both Distance and Direction or as Linear and Circular aspects. A center of a compas or a radius are Linear elements. So they can't be used to designates the Circle Direction property. Consequently, we should find what is the characteristic of the space Direction. A such definition will be the unique one for a circle. The circle postulate can rest a such unique concept. We can state the Circle postulate as follows:

A circle is the figure of a pure matter Central Symmetry

any other properties are the Central Symmetry consequences from where we can classified them as theorems.

- what + is + rule + of + law + what + is + the + conseqence + in + abscence + of + rule + of + law (Ethiopia)

- centre symétrique classe de 5ème (France)

Practical Exercice
From a given point marked on the ground, it is asked to two or many children to have to placed themselves around this point. They will do in such manner that they expressed by their location what is the meaning of this point on the ground as a Central Point. It is to say that the children have tp expresse their feeling about the Central Symmetry.
There is a corresponding inverse exercice.
It is for somebody standing at a fixe centre and then to place everybody around him in such manner that the whole form a circle around it center. It wild be done in varying the distance or the circle radius.
All these exercises will be an amazing and educative ones if there is an equipment of photos and some computer that allow to verify rapidly the circularity of these field events.

The Central Symmetry knowledge is a natural capacity of everybody that have to be maintained in conscience activity. Because this latter is source of human physical and mental equilibrium. Note that the central symmetry is an everyday capacity of wild annimals.

Example of how to deduce from the Central Symmetry postulate
the usual figure of any circle

- central symmetry (Latvia)

the central symmetry is a practical postulate that can be used in applications. A central symmetry is extended to both the linear and the circular space aspects. For example, a point as a cental symmetry of a system, can be verified by any other of its points that it has necessary a central symmetric point. Also, it can be verifyed with any axial symetry by angular equality between 0-180 degrees.

1) - The central symmetry in the universe means one unique point (C) defining a Center point. Extending this latter meaning, the universe is necessarily as a space having the property of being in discrete location points. Without the Fact of the perfectly defined Central Point in the universe - e.g. the space as a Continuum - there is a contradiction to the the possibility of Central Symmetry.
2) - Thus deducing from the Central Symmetry One Point it can be defined the reality of any one another point (P) in the univers. Now refering to the Central point (C), it can be produced a corresponding point (P') according to the Central Symmetry property.
3) - Being a space of discrete point the direct consequence of the Direction (CP) is that it is composed of a quantity of discrete points. Consequently it can be deduced the property space Distance equalilty as:
From there, necessarily, any other point (Pi) forming as (CPi) constitutes a circle of this radius distance. An another importance of consequence is that with the reasons of such deductions we can state that the universe is necessarily a spherical space. Out of the Central Symmetry postulate, that is to say, the beyond-the-universe space, is nothing else than blancking of reason for knowledge. No logic of law can allow us to name sommething with the Nothingness term. This is the universe as the Whole concept.

This is an example of what is deductive consequances that can be done from a true circle postulate. Without the Central symmetry, there is blankness of reason. From a such postulate unbounded consequences can define what is the wealthy circular property in the universe space.
From a such perfect central symmetry without no Form because there was only space Direction, we can deduce that there was necesssarily a matter process for space Distance definition. Space as Direction and Distance is the logic of the universe as form constructions. Therefore, there was necessarily one Beginning from the pure central symmetry for the Distance Transformation Generation.
Therefore, there is logically in the universe the Beginning of Construction Event rationally defined in Dakhiometry as the apprearance from the Circle property a relationship corresponding to the Square form.
From there any form, included the Circle, the universe uniqueness realities can be constructed as precise structures of forms in space.

- plato and the theory of forms (, UK)

- plato theory (Colombia)

On the Circle or Mathematics an Physics ignorance of space

About Plato theories
- Plato's inventions (USA)

- the world of form (Thailand)

May be, from the Plato's compass was intituted the famous circle definition. From there circle formula are defined by a radius. It is only a creation from "idea".
Because practically and more basically, a circle should be accessed by its diameter. Remember that manufacturing of tubes use a diameter to specified any tube. And the first possible measurment of circular form is the diameter. Also, astronomy uses diameter of heavenly bodies.

Property of space in Dakhiometry
A circle can't be construct with nothing else than according to the circular properties.

Plato tell that the world is based on the differents geometrical figures included the circle. But this universe space description shows that he don't know really what is the circular realm because a such theory is only the Linear universe.

Because when he tell that geometry should be constructed with a compass and a straight edge he din't be in consciousness that a compass is not a circular device.
a Compass, is only a LINEAR device!
Therefore, the expression "compass and straight edge" is equivalent to "Staright edge and straight edge".

On this next figure, is shown the real basic structure of a compass. A compass is no other thing than a straight segment. It is a Linear structure. The rounds done with a compass are only conventional symbols of Circular Circles produced by a linear tool. While a square is really a real linear figure constructed with linear tools.

Definition of a circle
A circle is a structure of space locations in Circular Succession. Nothing else out of this circular succession belong to a circle property.

Thus, the definition of a circle as points at equal distance from a center point, is only a figure of the Linear Realm. It is why most statements on circle are done using its radius. This is the proof of Mathematics ignorance about the basic difference between Linear and Circular properties.

a) - According to these usual errors about a compass, one can draw many geometrical figures with a compass ignoring that one is using only a straight edge structure and the circle are there only a conventional figure of "equal distance from a center point".
b) - In practice a square can't be constructed using only with the property of a circle as circular points in succession. Because this circular structure is in fact the Direction Structure or more wellknonw tell as Angular Structure.
c) - From a circle there is uniquely one possible transformation: the squaring a circle. This latter is the even from there Linear realm can be revealed. It is the event of linear Direction that allows to measure the Angle in space. Angle can be defined only when straight line exists in conscience.

For example, to draw a square with circle, we need first to define at least a 90° angle or its multiple. We do that because, we KNOW yet what is a direction lines. But with only the real circular structure we can't know what is a straight line.

From Ignorance of the Circular realm,
appears the empirical mathematic of Exhaustion and Convergence methods

Ignoring that space is characterized in two aspects Linear ans Circular, one meets difficulties of knowing what is a circle.

There is the famous problem of defining the circular structure as for example the circle diameter and its disk aera. A mysterious and magic key of transformation appears in the whole world as the unattainable God with the name Pi.

From a such God, Mathematicians are running in a vicious circle as the Achiles and the Tortoise race.
For this purpose, theories are built for the know how to catch a ghost as follows:

a) - Zeno's Achiles' axiom
Running after, you can't catch nothing if you are enough doing the half of the necessarry way to be equal the job.

b) - Archimadean enhance axiom
To catch an aim you need to do successively more than a half-way toward the goal. You will then going byond it.

- Archimedes' + principle + is + not + precise + enough + for (Turkey)

In fact the preciseless of this axiom is only because it is an empirical statement. Discrete Space is the fullness of precision. When nothing is known one use to think "more than and less than principle". It is also the case for the Ptolemy theorem of inscribed quadrilaterals where the precision can be shown.

According to these famous and applied theories, here is how Archimedes try to catch the shifty God Pi. It is compare there what are the difference between a Half-a-way denoted as (MZ) versus the more-than-half-a-way denoted as (MA).

- pictures of plato and his inventions (, MicroSoft Corp, USA)

Actually, the two segments of a nice compass device is only one segment of the circle radius. It is why one use to define a circle with its radius instead of his diameter. This later is what in astronomy pactise we need to know and can be measured directly.

- Plato's belief in law (, Canada)

- ignorance exhaustion death (FHCRC.ORG, Fred Hutchinson Cancer Reasearch Center, Seattle, Washington, USA)

- Plato's inventions (California, USA)

In this figure is shown (OB) as what is a Plato's Compass.

- Plato's inventions (, Canada)

- Plato theory of forms (, UK)

- Plato's belief (, Madison Wisconsin, USA)

- Plato theory of ideas (Latvia)

All object construction of the universe are done exclusively according to the universal laws. Whatever are the multiplicity of forms any construction is then deduced from the universe space structure properties. Human is no more different from any simplest object. In fact nothing is really simplistic because they are perfectly organized by the universal laws. Perfect means here according strictly to the Facts of universal laws. Human capability of thinking is no more than a form property of law construction as well as a falling body or a chemical transformation of any matter even if the thinking seems to be a more complex transformation process. The human thinking is only the fact of a complex transformation mode inherent to any human and is being basically impress in human as his own internal property.
Therefore, human Ideas are not something outside to the human whole construction sytem. Human ideas are facts of internal structure of the alive. For example, the fact is that anyone can intuitively know any elemental form in the nature even if he can't named it. It is because, without no form recognition nobody can't neither behave nor move as he need it in evryday life.
that universal laws means that strictly, nothing is outside of any universal law. It is why there is no Nothingness. Nothing is in the Nothingness according to the Nothingness should define No Universal Law because anything is necessary properties from universal laws.

- Plato forgotten river (, Tennessee, USA)

- philosophical theory of forms (USA)

- Plato the divided line summary (, Arizona State University, USA)

- theory of forms non material (Missisippi, USA)

However, forms are Quantities the property of concrete matter. The belief that ideas are forms, therefore cunfusing ideas with quantities, drives to Dedekind and Cantor to invent from their imaginative ideas, that infinities are also forms, the numbers ones. The Euclidean Line is also a Nothinness in contradiction when designating the material space line. In brief, since millenaries, Mathematics is manipulating Nothingness and ignores what is the concrete forms of space reality. This is the science Continuum dogma background.

- Plato's belief knowledge chart (, Blagoevgrad, Bulgaria)

- examples of what is the difference between reflection and refraction in math (, USA)

- math pi examples in middle ages (, Hawaii, USA)

- What Did Zeno do for math (, USA)

- maths example -lateral thinking enhancing vertical thinking (, University of Botswana)

- image of difference between open-loop system and close-loop system (Russian Federation,

Ligne droite et courbe.

The belief is that Linear tool can reproduce the Curvilinear realm.
Difference between Zeno's Clasical Exhaustion (Mz) and the Enhance Archimedean one (MA), is that Zeno propose to do exhaustion with the preceding half-step while the Archimedean axiom states that it is done with a little more than a half-step. But both are unsuccessful courses.

Also, the Plato's Compass as a segment-OB Principle.

The Archimedean exhaustion process can't never be achieved. because simply, we can only exhaust a polygon toward a PRECISE GIVEN goal and not toward exactly an UNKNOWN thing as the Circle-to-be-found. That is to tell, the polygon method is to catch the shadow of a ghost.

1) - In Dakhiometrie the Archimedes' axiom as {(n.a)>b} is only a consequence of a real basic principle. It can be only a theorem simply proved.

2) - The way from points A and B can be precisely decomposed and fully "exhausted" with the space structure. Point (A) is precisely equivalent to point (B). But only using the Circular property and not the linear archimedean exhaustion step.
Why is there a such result?
It is because in the space structure, there is the immortal presence of the Space Constant!

- moment + of + inertia + circonference (Ireland)

- what + is + the + definition + of + mathematical + term + absolute + difference (USA)

- points + to + note + when + constructing + concrete + surfaces (Guyana)

- mathematic history model on how formula of "area" of circle was derived (USA)

- Plato geometry (, Egypt)

From the biginning of human concept on space there is only linear mode of undestanding space. Even if Plato tel that Geometric problems should be resolved with compass-and-straight-edge, he was telling only linear space meaning. The classical impossibility of resolving the squaring a circle and the angle trisection are example of ignorance of the universe space or the matter space. It is because the angle is a circle property. The origin of space ignorance is to be unconscious that the circle is not a form amongst so many other linear forms. So, it was a Plato's errors to tell that tne universe is an assembly of triangle, squares and polygones as layers in spherical sky.
True knowledge of the universe space should rest on the foundation that the circle is not a form but a logic-of-form. The transcendent logic which we have access to, is the Space Constant of Form Transformation exposed in this present text.

1) - circumference definition
The circumference is composed of the number of discrete elemental matters disposed successively in a same central symmetry, two by two. Thus, a circumference is the "area" of a minimal circle crown.

2) - The summation of all the crown "areas" of a circle is then the total "area" of the circle disk.

3) - The "area" of a circular disk is given as :
Theorem :
The "area" of a circular disk (S) is the summation of all the circumferences of concentric circles included in the "area" given (S).

- concentric merci device (India)

- animated bc calculus (USA, Illinois IMSA)

- unfull circles (, bm, UK)

- Archimedes measurment circle high resolution (, University of Crete)

The exact process for  Intégral calculus of circle "area"
Let an integral calculus process of measuring an "area" (S) of a circle (C).

Let (D) the diameter of elemental matter crown and (dx) the minimal length of an elemental matter.
Then the "area" of circle (C) is the summation of all the crowns of diameter (D+dx). Provide that D varies from zero to CD.

- formule mathématique incorrecte (Canada)

Actually, this following formula is nothing.

S = Sommation [ (D+dx).Pi.dx/2 ]       (aa1)

D varies from zero to CD

The disk of diameter D is decomposed to concentric circles, according to elemental succession (dx). The aera of the disk is then the summation of all these concentric circles. The corect formula is as follows:

Summation all perimeters =
Pi[Summation from zero to D of ni(dx)]       (001)

This algebric formula is only an approximation of axhaustion method.

- uniqueness + of + the + reciprocal + proof (USA)

This theorem in direct proof is based on the formation of a circle "area" by circumferences of discrete matters.
The inverse proof is as followss:
Does a circle composed of circumferences as defined in the direct mode ?
The answer is yes.
According to the theorem of circle Chords. This latter proves that a circumference of a circle (C) allows to determine by unique manner any points of its radius as belonging to one cocentric interior circonferneces. Therefore, any "area" of a circle can be decomposed into uniques interior and successive circumferences as proved by the direct theorem. The reciprocal is True.

- different + things + built + on + the + basis + of + knowledge + of + pi + in + ancient + period (United Arab Emirates)

- "differents" + values + for + pi (Sweden)

- remote + control + robot + "construcyion" + set (Thailand)

- does + the + perimeter + of + a + polygon + convert + to + a +limit ?(USA)

An important question that needs a fundamental precise definition.

If matter space is a fact of absolute locations of immutable elemental matters. Then, a line composed of matter elements is necessary composed of one elements aside an another all along.

Then, an ultimate side numbers of a polygon is necessary composed of a total number of elemental side lengths. Thus, a polygone has necessary a limit of number of sides and not of side lengths.

So, what is the difference between the successive elements of a polygon and the one of a curve ? The fundamental differences are:

1) - Polygon

1-a) - A such polygone limit is a set of sides that are structured as a polygon.
1-b) - The perimeter of this polygone is a CONSTRUCtION of elemental lengths.
1-c) - The differents different elemental sides of this polygon are PLACED one after the other. Each side is differently DIRECTED from the next one.
1-d) - The polygon is then a set of associated elemental Straight Lines.

2) - Curve

2-a) - A curve is also composed of a number of elemental matters.
2-b) - The length of this curve is a SUCESSUION of elemental matters. It is the RECURRENT structure of matter.
2-c) - Therefore, a curve is a whole ONE DIRECTION recureence structure. This direction is toward one absolude precise point. It is why a curve is located and defined by its center.

Measurement resulting :
At the ultimate boundary of a polygon and the circle perimeter, we have a seemingly elemental line. However, the problem is : WHERE these two lines should be surimposed as equality of form ?

Therfore, one use to think that polygon-circle equality is directely the consequence of a polygon being-a-line with this line staying directely on the circle perimeter. It is only a sensitive obviousness that don't rest on any reason even if multiplication of polygon side number seems to match. It is the same for the infinity descent method there is no logic reason other than a conventional obviousness. As there is no reason to allow the Archimedes' Exhaustion, this situation proves that there is some artifact in the convergence calculation process. These convergences do not drive towards a presupposed value. The proof is given by the Euclidean division algorithm where there is not a necessary end of convergence. And also, in the following exemple of the integral calculus where one ontains the value 3.1416 for Pi. A precise infinitesimal calculus, don't change there the result. Thus, it is really an systematic severe error due the convergence process.

Only the space structure concept, allows to define the difference between circular and straight line based forms.

In brief:
A polygone is a multi-direction line organisation. One name its perimeter as a polyline construction.
A curve is a whole ONE direction Recurrent structure that allow to define precisely an absolute point center.

A polydon polygon that is a particular space construction can't replace a space structure principle represented by a circular line. It is why the biginning of the universe construction happens from a circle mono-space-structure transmuttation that allows multi-direction constructions. Inversely, a construction as a polygon can't directly get into a basic permanent space structure. This is why the universe construction evolution goes forward on an unbounded way without never return back. Possibility of including circular forms as a tools amongst other forms can only be done through a Spatial Constant factor.

Aside approximate processes, there is no other means to precisely surimpose equality between straight lines and curvatures. This is a basic characteristic of matter space that obeys to principle of absilute absolute locations and non by random placement of matter in a nothingness.

- "polydon" with five sides (USA)

- "absilute" + value (USA)

- Which + of + "teh" + following + values + "of" + "ameasure" + quantity + shows + "teh" + "greates" + resolution (Canada)

Actually, it is done with a very low resolution apparatus that can tell anything...

- pi + human (Estonia)

- why + thus + the + value + of + tangent + function + did + not + touch + the + undefined + value (Philippines)

- vertex + determination + angular + resolution + basic (UK)

A fine rational definition of polygon vertex by the variation of direction measurements.

- discreet + mathematics + methods + of + proof + direct (Qatar)

- a + measurement + that + is + accurate + is + one + that + is + as + exact + as + possible + is + close + to + the + true + value Ccontains + at + least + four + significant + figures Cor + contains + five + decimal + places (USA)

- who + invente + pi + number (Dominican Republic) - value + pi + full (Spain)

- the + "mathamatic" + of + beauty (UK)

- atomic + "bonb" (Japan) - "bonb" + atomic (Morocco) - what + are + the + physic + of + tai + chi (USA)

Proof of the circle "area" formula as Pi.R2

- Holly + Bach + Remedy (UK)

- supernovas (Peru)

- how + does + the + formula + "area" ++ Pi + R + square + evolve + + or + come + about (Canada)

- que + es + un + mumeral (Peru)

- more + knowledge + circle + perimeter (USA)

- Planck's + length + proof (USA)

- definition + "spartial" (Singapore)

- having-a-concept-of-self (HongKong

- continuum + of + reality + escapes

- transcendent + pi (USA)

A Sparial Constant as real meaning of concrete construction beginning of the universe.

- To + what + extent + can + the + -rule + of +law- + help + to + establish + just + law (UK)

- absolute + location + of + k2 (USA)

- last + four + supernova + occurrences (USA)

- "spartial" + figures + geometry (Honduras)

- where + is + the + liberty (Brazil)

- prayer + wheels + erase + energy (USA)

- "discribe" + the + properties + of + gold (USA)

- is + there + any + thing + beyond + the + universe? (New Zealand)

- meaning + of + "spartial" (Kenya)

- exact + value + of + pi (Australia)

- pi + value (Costa Rica)

- physic + transformation (Denmark)

- "spartial" + organisation (Tanzania)

- proof + iterative + formula (Ireland)

- is + the + word + Phenomena + a + mathematical + term ? (USA)

- How + many + percentage + of + "Ligth" + is + absorbed + by + paint ?(Germany)

- What: +++ La + Vérité + est + toujours + l'idée + qui fait le tour + du + Monde +++ means (USA)

- archimdean + property + of + R (UK)

- what + quality + consciuosness + and + habit + process + is + all + about (Philippines)

- what + if + an + equation + had + three + variables (Canada)

- numeral + pi (Antigua and Barbuda)

- démonstration + surface + d'un + cercle (Mexico)

- Archimedes + "area" + of + circle + equal + right + triangle + circumference (USA)

- extending + a + known + perimeter + then + finding + the + new + perimeter& (USA)

Exactly tell. Extending a line, is a same line while extending a circle perimeter is creating a new perimeter. This the characteristic of the circular structure. Consequently the universe can be define with nique circle series.

- how + do + you + find + a + square + of + a + series + of + numbers (USA)

- all + seeiing (Argentina)

- finite + elemnts + analysis ++ calculation (Malaysia)

- law + of + conservation + of + maatter + during + a + physical + and + a + chemical + change

- indestructible + elements (USA)

- instruments + to + find + the + physical + quantities + of + "area" + speed volum time lenght density mass + "etc" + and + more (United Arab Emirates)

Y O U   A R E   R I G H T !  "H I G H T"  R I G H T !!!

- properties+of+the+matter (Chile)

- "spartia" l +summation (Kenya)

- proof + of + "area" + of + circle + at + first + time (Pakistan)

- when + was + the + first + "ewhaust" + system + invented (USA)

- "Formaula" + for + Density, Mass + and + Volume (Greece)

- "formaula" + to + find + image + of + a + point + with + respect + to + a + straight + line (India)

- "itegral" (Brazil)

- reseach on failure in using formulas to measure area (Maldives)

- animated area formulas (Philippines, Mindanao State University, Iligan Inst. of Tech.)

- algebraic formulas (Mauritius)

- exact area of a circle using integral notation (, Oregon, USA)

- measure circle "area" (Korea)

- 4d Singapore formula (Singapore)

The above summation formula (aa1) is the proof of how a circle "area" is composed of.
Formula: circle "area"
The above process uses ultimate elemental construction to define the circle "area". This present method is quite different from the Algebraic integral one itegral. The next figure figures out this summation process written in equation (aa1). It consists to refere on a measured surface of a square and then to deduce the circle surface according to the Space Constant obtained from the squaring a circle.


After the squaring a circle resolution, a Space Constant TT is known. This latter is the one and unique key from it all the circle characteristics are given. One can deduce precisely and exactly the aera and the perimeter of circle.

- circle "area" and perimeter (South Africa)

With a circle of diameter D we have:

a) circle Aera = TT(D2/4)

b) circle Perimeter = TT(D)

From relation (001), we get:

TT(D2/4)=R2=TT[Summation from zero to D of ni(dx)]

we get:
D2/4 = [Sommation de zéro à D de ni(dx)]

Let a square of side equal to D. It can be seen that the circle aera is:

Disk Aera = (Square aera).(TT/4)

The previous diameter D as summation of (dx)correspond to a square as:

Square aera = D.D = D2

More, the space constant TT, allows to prove a new algebraic theorem as follows.

Writting with the circle radius R we get:
(2TT).(Somme de Ridx) = TTR2
2.(Somme de Ridx) = R2

Theorem When a quantity (n) is associated with an elemental quantity (dx), there is a relationship between (n) and the summation process with (dx) written as:


- integral in mat (USA)

To be abble to verify this Algebraic formula we must choose good values for these data. It is done as follows:

Let L a given length. From there we can define L/n=(dx)

The more greater (n) the above formula runs well.

That is to tell
When (dx) is lesser than 0.2 then an integral and a differential equation can be of an approximation without to much error. This is valid for electronic signal processing using sampling analogic ones. However, a differential and integral calculus should not be considered as precise calculations. They are only mechanical methods to get the nearest value.

This theorem show how the Algebra is a product of human language. It can Never give an exact and precise solution.
While with construction in space, we can see immediatly the (ni(dx)) summation as a powered variation and is a curve. Because this formula is erroneous with low (n) values where the curvature is pronounced. While this theorem is a correct one for great (n) values or very low ones for (dx). It is because at these scales, a powered funstion is similar to a straight line.

It is the meaning of the summation equation (aa1).
The above summation of circumferences in a circle allows to know the circle "area". It also give the proof of the circle "area" formula.

- "Hight" + mathematics + proving + the + theorems (Russian Federation)

- 2d + space + physic (Argentina)

- definite integral formula using the method of exhaustion (USA California)

- integral calculus (Peru)

- circle + theorem (inventor) (Thailand)

Theorem of a circular disk "area". Statement

Provide that a line and a curve is a succession of elemental surfaces, the "area" of a circle is stated as follows.

Dakhiometry theorem

1) - The circular disk (C) "area" with a radius (R), is equal the total "area" of all the cocentric circumferences with radius situated between zero and (R).

2) - Inversely, all cocentric circumferences of radius (x) situared from zero to (R), occupy a total "area" equal to the circular disk "area" of radius (R).

An another equivalent statement of this theorem, related to the squaring a circle, is :

Dakhiometry theorem

1) - The "area" of circular disk (C) of radius (R) is equal the "area" of the square of side (2R), time the Space Constant denoted as (Pi/4).

2) - The "area" of the square of side (2R) is equal to the "area" of the circular disk (C) of radius (R), time the Space Constant inverted (4/Pi).

All these theorems need the Space Constant, only determined by squaring a circle.

The Volume of a Sphere

- Pythagorean + alphabet (Czech Republic)

The term alphabet designates the conventionnal elemental symbols representing the images or the sound that any human can reproduce to express some of his ideas during their mutual exchanges with the means of talking or reading. Then, you are telling exactely what Pythagoras tried to proceed mathematical concept as a human talking language. He did it whith with Numbers that are only conventional talking and writing languages.
Because the real intuitive mathematical notion that any alive needs to get conscience and knowledge is the pure space concept of himself and of his space envirronement. However, because the deep knowledge of space is too hard to get and also because drawing geometric figures was not so easy when lacking of drawing materials. For example, modern computer gives a great capacity to us to get more and more complex space figures. This is forbiden for the first human mathematicians. The Anciants can't but choose a way of expressing mathematics concepts with conventional languages. Thus, Numbers become the most used mathematic elements. From there Pythagoras invented the universe as Numbers. Next, Arithmetic, Algebraic and Analytic Geometry that was conscepts of space transformed into number langages, are means of doing mathematics. The basic difference between the first and the second method is the impossibility of the first to get precision in matter laws knowledge. Conventional talking and writing languages are separated with the pure elements of space by a deep lack of the first to get precision of matter laws. Precision is not an ideal of ideology. But precision is the property of space construction in the universe that is needed for human to go further into complexe constructions.

- numeral + language (Greece)

Numbers are really human invention as conventional language to tempt describing space concepts that are only length and distance existing in ratios for constructions. One can tell that space is accessed and known intuitively while numbers are human intellectual concepts. Intution is there the capacity to be conscious and to build knowledge on the universe because alive and any thing in the universe are constructions of the universe matter laws.

- object + or + natural + phenomenon + of + constant + value + used + for + reference + in + measurement (USA)

- la + sphère + pi+ nombre + énigme + forme + aussi + simple, + cachée (Belgium)

The KEY of the Beginning of the universe is the transformation of circular structure in linear possibility of object construction. That is to say construction is the beginnng of conscience and conscience is the matter of knowledge. Physically tell, beginning of construction is the possibility of measurements for interactions in construction.

From that nothing in matter space is hidden as mystery.
However when we talk about mysteries, it is only because of human limitation for taking conscience and getting knowlege on natural laws. Physical laws are simple because they are part of anybody. Thus when some physical law is difficult to know, even if it is very simple, this is due to some particular state of human thought.

On can tell that the mystery of the squaring a circle is due from a so long time where mathematicians had give up the effort of understanding the Space as matter. This gived rise the impossibilities of resolving some problems in Geometry. Geometry believes that human can get knowledge by conventional language and thus manipulates only abstract thought. However abstract thought are mostly imaginary and matter space knowledge can not be reached by theses mathematicians. Therefore for no longer, mathematics becames science of conventional language formalisms. These are the cases for Numbers, Arithmetics, Algebra and all what follow as their developments. Then, from simple natural laws, mathematics go on into the super formalism complication.

Here, the Space Constant is a KEY for a vast means for going through the space understanding. This Constant is not yet well received by the current world science and techniques becaue most of scientists may see there as a new receipts or tricks. Most part of you are interested in the old Pi of how it is irrational or how it is composed of decimals.

Here is an another importance of the Space Constant. It concerns how to get the sphere volume according to it.

Let a Cube (C) with the side equal to the cercle (C) diameters. We can operate as the obove procedure to proove the surface of a circle with the square one. Here we need to do in two times the Summatios of elemental lengths to get the cube volume. And from these results, a new form of the Space Constant give us the Sphere volume. It is done as follows :

Vol(S)<=>(Constant / 6)*Vol(C)
Vol(C)<=>(6 / Constante)*Vol(S)

In brief
According to the current notation about the old anciant's notation on Pi we can state the following theorem.

Dakhiometry theorem
The volume of a sphere:

The volume of the sphere (S) is equal to the Cube (C) of side equal to the sphere diameter, is given as:

Volume Sphère = (Pi/6) * Volume Cube

Proof on solid volumes and surfaces have more basic procedure not given here but always according to the Space Constant.

Thus the Squaring a circle is the most simple while it is the most fundamental KEY for space knowledge.

- relate + the + aera + of + a + sphere + to + the + area + of + a + circle (Duke-Energy corp, USA)

- sphere in cylinder (, Toronto, Canada)

In Dakhiometry it can be determined probably any surface and volume of solid. This rests on rational and universal basis. It doesn't proceed as it is not done with the Archimdes' Method. This latter is no more than a mechnical one as one found usualy in empiric manner.

This is a very interesting remark.
circle and square inscribed It is an important application of form transformation parctically useful in many industrial or architectural applications.
All solid volumes are spatially proved. From there, it is very easy to do form transformations related by a same volume or a common factor.
Here is a transformation cylinder/sphere according to a common circle diameter. This is spatially done using length proportions.
An interesting corollary:
The cylinder volume external to the sphere one is equal to the volume of the sphere external to the cyclinder one.

- circular has less perimeyter than square (Pakistan)

Actually, at same volume, circular perimeter and surface aure less than the corresponding ones of a square or a cube.

- largest + lateral + surface + "area" + sphere + cylindar(USA)

Right! Largest cylinder and largest cylinder lateral surface is a cylinder inscribed in a sphere. This cylinder is characterised by a square as its section along the central axis. This square section is inscribed in the sphere. It is an important matter space fact because this space structure determines the globe characteristics of any heavenly body.
The formula is easy. This cylinder square section is the square inscribed in the greatest circonference of the sphere. The cylinder axis length and its base diameter, are the square side length.

- What + is + the + formula + for + how + to + find + the + largest + square + that + can + fit + in + a + circle (USA)

- formula + for + the + maximum + square + that + will + fit + in + a + circle (USA)

- largest + cyclinder + inscribed + in + sphere + calculus (Canada)

This cululation of the largest cylinder inscribed in a sphere is done in the determination of the heavenly globe ring structure.
The maximal cylinder fitting in a sphere is seen in 90 degrees latitude for its height.

There are many practical situations where one need to put a square form in a cylinder one. It concerns mechanical constructions as well as for foodstuff use. Then, the cyclinder circonference time the space Constant factor give directly the maximum square perimeter. From there one gets the maximum side of the square that can be adjust through this cylinder.

The proof is simple according to the following theorem of maximal product:
Let a rectangle inscribed in a given circle.
The maximum aera of a such rectangle is reached when this rectangle is a square.

For a cylinder in a sphere, let us consider its section through its principal axis of symmetry. We know that the volume (V) of a cyclinder is : V = constant.[D.h] with D=diameter and h=(axis-length).

Thus, according to the above theorem of maximal product, the maximum cylinder volume in a sphere is such that:
D = h

Therefore, it is a cylinder with a longitudinal square section.

- pie+is+round + cake+is+square + pi+is+3.14 + what+is+cake? (USA)

... Convergence towards endless insatiated goodies for wipped cream cakes ???
... Help !

- painting + inscribed + squares (Spain)

Consequences :
Relationship between circle and its inscribed square.

- the + inventer + of + pie + formula (USA)

- carré + inscrit + dans + un + cercle (Belgium)

- Pi + relationship + of + circumscribed + circle + and + the + square (USA)

circle and square are linked together is positions of inscribed and circumscribed. In the case of a square inscribed in the circle, the same Space Constant is used to describe their relationships.
circle and square inscribed
On this next figure are indicated the notations used in the following. As for the case of a circle inscribed in a square analyzed above, we will use the same Space Constant obtained. This method consists of using a square as reference of calculation. This reference is denoted here as the square (T). The circle has the side (d) of (T) as diameter. And the inscribed square in this circle has its side denoted as (c)
With a such reference (T) the Space constant is the same universal constant equal to (Pi/4) with its inverse value as (4/Pi).
This Constant is use to write the different reciprocal relationship between the circle and this inscribed square.

Notation : (sqr) denoted as Square Root of (2).
Then, the relationships are given in the following !

Square (T) :
Pt = 4.d ; and St = d2
circle :
(P) and (S)
Square (c) :
Pc ; and Sc

For perimeters we have,

P = (Pi/4). Pt = Pi . d
Pc = (4/pi) . P = 2.sqr(2) . d

P/Pc = Pi / (2 . sqr(2))
P = (Pi /(2 . sqr(2)) . Pc
Pc = ((2 . sqr(2)) /Pi) . P

For aeraes we get,

St = d2
S = (Pi/4) . d2
Sc = (4/Pi) . S = (1/2) . d2
S/Sc = Pi / 2
S = Sc . (Pi/2)
Sc = S . (2/Pi)

It is important to generate these formula according to the method of starting from a square as reference to aobtain the Space Constant. This use allows to keep alive the method of thinking that consists of starting from a base, then unfolding successive reasons for developping construction. Remind that the circle and the square are directely linked together in succession of series. So, from a base of a square as reference, one can control the measurement of these series of figures.
In more, the use of the Space Constant from a reference, allows to easily memorize the different formula without being dependent to their formalism that will soon be a great confusion for scholastic teaching.

- impossibility + infinity + theorem

- nothing + in + the + universe + spawns + from + absolute + nothingness (USA)
You are right. The Matter Conservation from a Discrete and Finite universe, is a solid principle on that rest physical laws. Evolution is stricly matter transformations.

- pi + value + exact + convert + online + billion + value (Singapore)

Spatial proof
of the Recurrence as space property

- picture of fundamental counting principle (USA Washington dc)

In the case where the universe is a Continuum, there is no distinctive capacity for human and nothing can be counted. Counting is the property of matter discretness in absolute concrete space.
On these bases, the universe measurement rest on the logic of Succession. It is why we can know space as the Near and the Far in precise and exact manner. Knowing the Near and the Far is no other thing than knowing locations by Distance and Direction quantity. According to the discretness any Quantity is unique. It is why uniqueness of Space is necessarry know in exact and precise manner. Therefore, quantities has the property to be known Successively.
Counting is the recognition of space discretness property successively accessed by human. Also, we acknowledge motion according to the successive discretness Fact of space.


- fundamental counting principal (USA Virginia)

- numbers + in + displacement (Spain)
This is the just new concept for counting, quite exactly what we must understand about the human fact of counting.
While from the beginning, human was concerned with language invention for their idea communications, the Anciants until modern thinking was trapped in language systems. Thus, it is generated the known natural number series. This latter is coagulated in an artificial formalism where they tempt to given somme imprecise foundation with recurrence and induction rigid principe and then created some basis for Number concepts. It is a poor formalism figure of : 1, 2, 3,... N wher many mysteries are built around it as Incommensurability, Irrationallity, Transcendental Number also with odd things that mathematised strange knowable Infinities and Nothingness.
Numbers are ideas for movement that are facts of matter space extends. These are the only fundamental reallities that are materials for human conscience. Then Recurrence is the matter property generated by the space reality.
What does human do when he is counting ?
As for animals and for all animated beings, everyone when he is exploring his environment, need displacing in the space. It is the same basic action when he is counting. He is doing an EXHAUSTION of space. When a farmer is counting cattle, he is doing as said above. He is then exhausting this particaular space that is the total cattle space. The basic mode of counting is to use movemant to displace. To be able to exhaust, you may displace yourself or you may displace all the cattle. This the fundamental fact of how to know a space extend.
Thus the natural number series is only a very schematic language figure. And it is a harmfull habit to take this writting formalism as a mathematical model from there all the Arthmetic and Algebra are built.
The only foundemental counting or space exhaustion is to get only the real meaning of the Recurrence property of space and motion. The following text is describing this Recurrence concept.
Now we can retain the pratical Natural Number series, but we must see counting, movement or exhaustion as occuring only of space forms. There is no fixed 1, 2, 3,... But there is the basic concept of the Unit. That is to tell, There is the uniqueness of of the concept Unit but there are multiplicity of Unit forms. And it is the Reccurence that allow multiplicities. That is, the Unit is multiplicity when one tell : 1 apple, one table, one cake, one meter, one day,... ect.
Mathematical application :
1) - It is a good use for mathematics to take the Space Constant as a Unit.
2) - Also, the Unit can be the Square Root of any numeral particularly the Square Root of 2.
3) - A square or a circle or any other figure form of any dimension, can constituted an Unit.

It is why one can use an International System of units and all other different conventional measuring unit system.
En brief:
As it is shown in the following, a ONE unit can start with any dimension and then one can use it to make a space exhaustion succession. As matter is fundamentally decrete, the Recuurence is a space exhaustion succession that does never mett any hole in space. Therefore, there is no Irrational, no Infinity. The Recurence is a precise scanning of the universe fullness.

- ULTIMATE + pi + calculator (Malaysia)

- discrete + mathematic + prove + one + plus + one + equal + one (Malaysia)
You are right.
The ONE concept is the Unit. An Unit is alqays an immutable Unit. It is why at any scale there is the possibilitlity for measurement, because there is there a Unit.
Now, one apple plus one apple is equate to two apples. Because, here it concerns the quantity of a particular object.
Therefore, the Unit is the beginning of the counting or the movement process and the succession of the immutable Unit is the contuity of the matter quantity as a length or a volume,...

- situation + when + exactness + with + pi + is + necessary (USA)

- False + void + of + universe (United Arab Emirates)

- impossibility + infinity + theorem (USA)

- is + the + world + a + big + "mathamatic" + problems (USA)
Because it is absolute finite space the universe is a big Solution. While for human, because he has to walk along the knowledge Way, the World is a great Problem to solve.

- what + is + the + quantity + of + motion (USA)
Physic defines momentum. However, as recurrence is the basic principe of motion, the basic notion of the recurrence is really the "quantity og motion". Thus, the following analysis are how to figure out this quantity of motion, relative to its quantity.

- basic + parts + "og" + triangle (India)

- pi ++ pattern (Autralia)
Not only the motion aspect of the recurrence, this latter is the fundamental principe that allows construction of spatial forms. Thus, it is a just notion when telling the following recurrence relationship as "patterns". Because, understanding recurrence allows to know how there a different forms in plane and 3D figures. Therefore, the surfaces and volumes of solids can be WHOLLY deduced from this recurrence base. In Dakhiometry, all the elemental forms are precisely known from deduction, starting from one spatial base.

- construction + of + the + universe (Estonia)

- what + is + fundamental + mathematics (Croatia)

- meaning + of + space + prove (Philippines)

- pi + rational (Switzerland)

- rational + pi (Nepal)

- how + is + pi + used + in + mathematic (Hongkong)

- mathamatic + definitions (South Africa)

- foundamental + logic + equation (Hongkong)

- the + continuum + concept (Canada)
We can define the difference between Continuum and Continuity.
Continuum is and old concept that comes from the indefined space. No lacation can be measured in this latter. Thus, the impossibility to get a measure in a such Nothingness is the origin of the Continuum concept. The continuum is therefore, a monotoneous Nothing because one can't also nemed it, because a Name means necessarry a Definition. Thus Continuum means coagulated, fixed, a One as death.
The Continuity is the property of a dicrete matter space. Discrete matter means possibility of differences. This latter generates Changes. Because discretness of matter is a permanent Fact then, the Chnage in matter is an unbounded Fact. This drives us to understand that the Continuity is the property of the unbounded Change in the universe.
In brief, Continuum is the monotoneous coagualated World. While the Continuity is the property of the Change in the universe. Finally, in matter there is the basic Recurrence Property of Change.

- universe + as + a + whole (Ireland)

The unique matter in the universe is both space and motion. Matter is dicrete thus, it is necessarry a finite quantity. On what foundation does the motion come from ? It is not sufficient to tell that motion is energy. It is only a tautology. The root of motion origin is in the discretness of matter, without it there can be the universe construction. Thus we there the key of opening the door for movement. It is the RECURRENCE in matter.

Recurrence definition :

The Recurrence is the Unique and Discrete Matter property to be abble to represent the fullness in the universe.

Thus, the Recurrence is the expression of the fullness of matter in the universe. It the matter is unique, this means that there is nothing else than matter.
Practically tell, the recurrence means that matter can succeed in discretness, one after the other without no rupture or no fault. And when matter is in recurrence property it appears as movement phenomenon.
Nous are going there to make the proof of the matter space recurrence. The contnuity of space is in the logic concept of successive spatial figures that are independent et distintive between them. And the continuity is expressed as the perfect relationships that link together these independent figures. Thus, if a series of figures is formed successively in the continuity of a law than we have proved the space Recurrence.

Resume the preceding analysis on relationship of a square inscribed in a circle. With this elemental property a spatial series will be formed.

Space Recurrence
This figure represents a series successively formed by square inscribed in a circle. Both are linked together by the Space Constant obtained from tha the squaring a circle.


sqr(...) means Square Root of (...).
Let denoted the Space Constant as : k = (Pi/4)

Pt = perimeter of a square (t) as reference of transformation
St = Aera of this square (t)

P1 = Perimeter of the circle inscribed in the square (t), with ordinal 1 in the series
Pc1 = perimeter of the sqaure square inscribed in this circle (1)
S1 = Aera of circle (1)
Sc1 = Aera of the square inscribed it this circle (1)

In this next notation of this series only the ordinal is changed.

- this will be pastulated (, USA)

- "Sqaure" + side + length + to + diagonal + length + relationship (Canada)

The preceding analysis on square inscribed in a circle, allow to establish the formula of the elemnts of this spatial series.

For the square of reference (t) :
Pt = 4d
St = d2

Then, the perimeters and the "area"s of each series elements can be deduced as follows :

P1 = k . Pt
Pc1 = Pt/(sqr(2))
S1 = k . St
Sc1 = St/2

P2 = k2 . Pt
Pc2 = Pt/(sqr(2))2
S2 = k2 . St
Sc2 = St/(22)

P3 = k3 . Pt
Pc3 = Pt/(sqr(2))3
S3 = k3 . St
Sc3 = St/(23)

... and so on.

Thus according to that the recurrence reproduces the same property, here is the Space Constant, a general formula is as follows when the successive ordinal take the one of the natural series number N :

Pn = kn . Pt
Pcn = Pt/(sqr(2))n
Sn = kn . St
Scn = St/(2n)

- traducir + "precurrence" (, Mexico)

Reciprocal :
From these equations the reciprocal precurrence recurrence process can be written. Thus, from a square inscribed in a circle of ordinal (n) it can be established a same system in any ordinal order (t). The recurrence step is well ordered. It is written as follows :

Incribed square in circle reciprocal recurrence
Pt = Pn / (kn)
Pct = Pcn . (sqr(2)n
St = St / (kn)
Sct = Scn . (2n)

The Recurrence process in direct et reciprocal modes in space, is fully established. In this example between a space (t) an (n) the recurrence defines the absolute Fullness of matter. The exhaustion between (t) an (n) is quite rational and precisely defined in any direction of the recurrence process. Thus we have proved there that in space the movement and its energy aspect, is completly and precisely defined, in any direction, without missing any part as fault or hole. The space is the a Fullness of rational matter.

With this series of value,
a precise Space Constant is necessary.
Thus, empirical value of Pi is irrelevent to produce this series because the circles and squares will no longer remain related between them.
Note that only the spatial figures are basic. The above numeral relationship are only used for a more familar view easyer recurrence understanding.

In these proof are used Arithmetics and Algebra means to establish formula. But the real optimal proof can be done with the full space elements constructions.

However, this belong to the Dakhiometry method and I can't develop it there. Knowledge of the elemental operations of transformations - the addition, substraction, multiplication and division - are needed.. The reason is that the current mathematics are narrow limits that can't allow larger knowledge extends. The Dakhiometry rests on basis that one have to get without which which condition, mathematicians should remains in mathematics of receipts and tricks.

- four + sytem + to ++ "which" + earth ++ belong (Canada)

- geant ++ square + root (Belgium)
In fact the square root is also a basic space constant.
On can see that succession of squares with circles mutually inscribed, are succession of circles and at the same time these such successions of squares are successiveley done by doubling the preceeding "area". Here also, the square root of two, is necessarry rational length, otherwise these succssions can not be true. The "area" doubling will no longer be precise if square root is an irrational quantity. This space structure of square and circle inscribed and circonscribed figures, is a DIRECT PROOF of the rationality of square root.
The above recurrence proves that matter space is the fullness of matter where space can be wholy rationally measured. This fact emphasized that Numbers are really langage products that are only approximative space property representations. It is to conclude that Numbers itself can never be space materials. Therefore, incompletness of langage generates odd thing as irrationality.

- theorical + mathematic (USA)

- Do + you + favor + strict + construction + of + the + law ? (USA)
Only spatial construction can truly prove a law. In space it can appear direct abd reciprocal logic that allows a complete proof. Everything that is do not belong the a structure is seen as a false datum.

Conclusion :
The figure representing this spatial series is the unique direct fondamental proof of the Space Recurrence. And the Recurence concerns the reproducibility of the spatial relationships between circles and squares according to the tha Spatial constant (k). This proof is done in two dimensions space. It is the basic law expression. It can be also extended in the three dimensions when it concerns the solids to express their volume and surfaces. This is then the proof of the total Fullness of matter in the universe. This cancel the different old hypothesis of hole, Nothingness, Infinity and Irrationnality tricks.

The different formula written here are only verification, and is given only because one use to understand the recurrence with the natural number series. However, the spatial construction is only the real valid proof.

Note that this series is succeeding in decrease order and it is denoted as the ordinal in subscripts and not on the power of perimeter and "area"s values.
In this example the beginning of the spatial series starts at any value of the square (t). But owing to the reciprocal of the Space Constant (k), the analysis can start at any beginning value and at any direction of this spatial series. In consequence, this spatial series is reciprocal. It is not necessarry to prove the preceding or the succeeding elements as it is need in arithmetic natural number series.

This spatial proof of recurrence is most fundamental for the motion knowledge and it allows an easy understanding of recurrence end motion.
Discrete matter is composed of the ultimete immutable elemental dakhion. It is from this element that the concept of ONE represent the matter unit (1) in the natural number series. It is useless to try to converge this spatial series toward some Zero that is only language convention. And seeking a zero in matter is a direct contradiction of a discrete matter principle.

There are numerous spatial series that can be proved in space. An example is given with the Numeral Generator that is given in an another page of this site. It is directely an easily constructed from space figure.

- there + is + no + void (Honduras)

A main view point you have.
The Dakhiometry Recurrence is a quite different from the current Algenraic Algebraic one. This latter is a narrow definition of the natural number series as an artificial langage creation confused with the basic matter property of motion.
The matter Recurrence is what allows movement phenomenon. Movement happens anywhere, at any location and ends where it ceases. Thus, the recurence or induction defined on the natural number series, is only a formalisme of automatic mechanic repetition that starts and ends as stated for the N series.
One can see that the Dakhiometry recurrence is here applied and illustrated by a circle-square system, at any if its origin. This is the pure basic Recurrence matter property. And the main proof that it shows is the Fullness of matter in the discrete universe. As you tell it : there is no Void in matter of the universe.

- distinguish + the + difference + between + an + "algenraic" + expression + and + "a" + algebraic + equation (USA New York East)

There is no difference because Algebraic is only a product of conventional language and is not a mathematical science of spatial structures.

- manipulate + reality + throught + quantum + mechanics (New Zeaaland)

- do + all + mathematicians + agree + on + how + N + is + defined ? (USA)
Definition of the natural number series N are yet narrow. It is clear that the recurrence and the induction principle are not very clear as concepts. This N demonstration or rather as definition are as most Algebraic proof. They are definitions or axioms that are only formalism conventions. Most of proof are not as a true proof should be.
For example, the present proof of the recurrence is a true one. This proof is complete : succession, order, contuity without rupture, directions and localisation of element that allows counting quantity. This is the Recurrence property that generates the Natural capacity of COUNTING for human when he use language to traduce the recurrence by the natural number series. It is the Recurrence that allows to understand what is human counting. It is also for tha the animal one and surely in the mineral where without capacity of counting there should not the possibility of forming cristall network.

- anthropomorphism + in + life + of + pi (Austria)

- d'où + vient +l'univers (Canada)

- What + is+a + Foudamental + Counting + Principle (USA)

- set + is + infinite + if + and + only + if (USA)

... if its parts are infinite.
1, 2 and 3 are parts of a set. Any set in the universe is countable. These counts are necessary discrete to be able named. Therefore, according to this discretness, no part of the universe is infinite.

- diffrence + between + open + cycle + and + closed + cycle (Saudi Arabia)

This a quite rational differentiation of concept.
Even if matter is a finite quantity concept, the formed universe is a open cycle. We know what is the usual system control using feed-back. In these theories the open loop system is only a class of closed loop process. It is because what human can know is only closed loop system, a model of a condensed matter. It is why the Gravitational obseved on Earth is an error when it is stated as an universal law. The whole universe do not belong to a system concept class. Construction processes of the universe is an open one and is a logic inscribed in our thought.It is the Recurrence process, the life open construction.

- open + loop ++ mode ++ meanning
Because the universe existence is formed with condensed systems. Each one is a particular independant and unique system. This is according to the uniqueness of space location. Therefore, in any of condensed system, every object interior to it is linked to the other one. They are linked because of the formation mechanism that bound all the matter from an initial cloud of elemental one. Because every things are linked together with this whole system, no one can be considered as an isolated objetc. This rule is valid for any apparatus produces by man. Then, an electronic system uses to proceed by close loop method. This latter means that this apparatus is linkec to its environment where it has an input and an output.
Now, considering the whole universe, this latter is not an objetc or a system. A whole is governed with principle. The universe is the property of the Unit principle. Then, a whole is unique, it is the logic One. We can not tell that a whole is alone this expression is a language error. Thus, a whole is the logic One. This latter is only an articulation or the elemental logic. Therefore, a whole can exist without the need of linking with any environment. The unit principle allows the logic of a Whole to work without any loop, neither with his exterior nor with his interior because for the whole universe, there is no interior nor exterior. A whole is a whole. There is nothing to add in or to substract from.
With a such logic view of the unit principle, it is easy to understand now why despite the matter is permanent, the life construction in the whole universe can be a wealthy unbounded process. This is the extended concept of a simplified open loop definition.

- what + is + the + value + of + finding + rationalist + proofs + for + the + existence + "og" + GOD (Montserrat)

The absolute logic of reasonning is as follows:
If physical laws are proved and with experiences corroborated then according to logic of existence, nobody can prove the true of non-law.

Fundamental facts of the universe is its Permanence and it Beginning of construction in condensation of discrete matter. These facts are logic corroborated by observation of discretness reality. And also, these fondation are unboundless fertile for knowledge of the universe existence.

Therefore, no proof of these facts as false or untrue can be produced according to logic reasonning.

It is why the Permanence of matter and its own beginning of the construction process can't cohabit with the imaginary reality of any Creator of the universe and its whole contains.

Man, the authentic Creator.
Remind that square and circle are
immutable universal objects.

- logical + cohesion + first + cause + universe (Bulgaria)

- Beginning + of + Universe (Hongkong)

- who + was + the + creator + of + mechanical + universe? (Turkey)

- spontaneous + matter + creation (USA)

- equation + proves + no + god (UK)

The circle is before the universe and is the permanent structure of matter. Every thing and We, are made with the wealthy circular structure. Thus, each of us is not only the stars dust but more fundamentally, we are also before the universe. Therefore, the universe and each of us, are never created. circle is not god becaause it is a basic structure amongst other ones and what rests on circular structure also can't be god. Inversely, all this Whole itself can't be god because god need not to create himself when the universe and human are created. As matter is necessary permanent and this Whole is god then, a god creation is only a feed-back action in the Whole. His creation is necessary a closed loop sytem where the Output human acts on the Input god. A such god can't never be a Creator because he is at the same time created by his creation. In any way that we do reasonning on god man sticks like glue to him. Therefore, Creator and Creation are only ONE person. This ONE is not the famous UNIT but this one god is only te man hiden under a mask.

In summary, In the situation of a permanent universe where a Creator can't create a Creation when this Creation can simultaneously create his Creator then,

A possibility of Creation is a situation of severe contradiction the existence of which forbids us to think.

- Two + only + things + touch + infinity : + human + stupidity + and + univers (Italia)

- Tao ++ how + to + draw + the + start + of +evolution (Australia)

It is an exact real fact that we can draw the start of evolution of the universe. Drawing and explaining this event is a possibility inscribed in our thought.
Exactly, at the starting of the Beginning, we all, in the past and in the futur, are being witness to this event. There was really no form because at this moment, there was not yet any form. However this event is in the permanence of the matter properties. So we can draw and understand the Beginning because, it belongs to our thought logic. It is really such. In next time, I will expose the proof of the equality of the circle and the transformed square surface. There is only simple elemantal logics. The logic of the Recurrence that allows the starting of only 1, 2 and 3 then, the proof is done ! It is simple, a supreme simplicity of the Beginning where life was born. However, this simple proof can be understood only with new concepts. What are exposed here in this text, contribute to this understanding.
You are telling the Tao, it is a just physical image of the starting universe. Because the Anciants had draw the symbole of the starting visible motion in the universe when they established the visible rotation of the universe in the form of the Yin-yang logo, due to the beginning of matter interaction for construction.

- UNIVERSE + AS + A + WHOLE (Former Czechoslovakia)

- about + the + origin + and + evoluton + of + the + universe (United Arab Emirates)

The Total "area" (S) is equal to the "area" of an ultimate elemental matter time the total length of all the circumferences.
This is the definition of a rectangle with length equaled to the total lenght of circumferences and with the width equaled to the ultimate length of elemental matter !
Isn't it a clear definition of discrete matter "area", even if it concerns a circular structure ?

This measurement by integral calculus is only valid if Pi is known. Obviously Pi is the Spatial Constant given by the squaring a circle. Any value of Pi can be used. But Only the Unique Spatial Constant is the True.

A such process is the more exact the more (dx) value is near the utimate elemental value.

- nothingness + and + surface (USA)

This is the JUST concepts to be differentiated consciously.
We are made of and we live fully in concrete matter space. Nothingness is an old human darl ignorance. Condition of rational knowledge should concerns the real discrete and concrete matter. Many old harmful ideas and believes should be quickly thrown out. Life is not only human tricks in closed loop group business. Condition of life is to get conscience of matter environment. Human has to get knowledge of the Earth characteristics and the environment characteristic of the Earth Planet. Everything is envolving, conditions of the alive is not to be asleep in a quiet coagulated eternal fixed Earth described by dangerous belief dogma. Stop being stupid human. A NEW WORLD vision is necessary. For everyone and eachone particularly, NO ALTERNATE WAY, is the condition to survive.

Consequence : the bad process

- Euclide + straight edge (Indonesia)

Why are integrals, differentials and derivative calculus generate errors ?
Analysis are done here for understanding thes calculations modes that are widely use in Algebra to define imprecise forms with curvilinear functions versus linear variables. For example they are used for describing field forces and for standard statistic distribution models.

- how + to + find + a + "area" + of + a + circle + "id" + you + only + know + the + circumference (Canada)

... if and id only... - how + to + work + out + the + circumference (UK) - explaination + of + line + types + in + drawing + and + geometric (Belgium)

- concept + of + infinite (Korea)

- foundamental + theorem + of + integral + calculus (Greece)

- integral linear disk area (USA, New York University)

Calculus of curvilinear aeras and volumes are usually done form graphic of linear Analytical Geometry. These are only acceptable as usual approximation. However using it as Mathematics exactness is a harmful systematic error. The most use of such approximation method as for example in the Fourrier analysis, should produce many unkown artifacts and bad interpretations. It is because the Trigonometric sine function is only a specific particular mechanical motion of a round solid piece. While in the nature, there is no "wave sine trajectory". There is ONLY, parabolic wave motion. The so many Fourrier function type used in analysis is really an artificial bad systematic measurement method.
In fact, the fundamental Space Angle is really a severe science ignorance. - integration calculus formulae for multiple function (New Zealand)

- linear vs curvilinear graphs (USA)

Unhapply, it is the usual mode of Analytic Geometry.

- calculus is only an approximation (verizon, Pennsylvania, USA)

Actuallay. Because:
a) - Calculus are done only in linear algorithms.
b) - These algorithms are only forms of the famous exhaustion method.
It is useful but give only approximative results.

Resume the preceding calculation of circular disk "area".
"area" of curvilinear functions

On left of the figure, bad integral calculus process for curvilinear function versus linear variable. On right, correct integral calculus when applied only to linear function.

It is proved that minimal circumferences "area"s are equivalent to the segment ones. Thus, all circumferences that compose the "area" of the circle (C) can be drawn as segment lenghts versus the circle diameter. The next figure show it axactly as a sine or cosine function.

The next bad process is to calculate the circle "area" accorfing to a curvilinear function versus a linear variable. The first thing that Algebra does is to calculate the "area" of the circle (C) with an integral calculus applied on this function. It is the same method used for exponential equation formalism that are only cosine function types. Example can be found in the Gaus, Fermi, Poisson,... standard statistic distribution functions that are only curvilinear function versus linear variables.

These calculus methods are quite erroneous and give only rough approximations. They are empirical methods and do not allows mathematicians to verify their results. Thus, their applications are generalized in any sciences.

Now that the squaring a circle is yet found we can show how these curbilinear calculus are only eronneous from there one believes that a use of infinitesimal object allows to go anywhere in forms of space. The following calculation of the circle "area" using curvilinear function versue linear variable, gives a quite high biasing result. And practical methods that use also such algorithm gives same errors. It prove that measuring the surface "area" to determine the Pi value of 3.1416 is a fact of empirical practise.

- Squaring + a + structure (USA) - history + of ++ mathamatic (Thailand)

- archimedes + circle + triangle + "area" (USA)

- WORLD + HISTORY + OF + PI 3.14 (USA)

- summation + pi (Canada)

- positve + and + negative + about + Archimedes (Australia)

- Archimedes + "area" + exhaustion + circle (USA)

- an + equation + Archimedes + used (USA)

- enigme + horses + eggs


This is a thing to be resolved. It is stange that form is associated with the Number.
From the Anciants there was known Form and Number associated in anything of the univers. Particularly for Pythagoras from what Numbers is the world archetype. Modern science comes from there. Therefore, everybody when looking to a form see there Numbers an inversely from Numbers temps to associate there physical object as sound or colors or the Good or the Evil that are also forms.
However, the universe is composed of only by discrete matter as location structures and as quantities of matter. Space structures produce forms and quantity of matter placed in these structures define its particular quantity. Therefore, a form is not characteristic of a quantity and inversely, a quantity can't tel what about its structure as form.
In conclusion
Perimeter and Aera are terms desinating both an object as quantities. A quantity is an uniqueness of any matter system that define a "matter mass" or its factor of mass. Thus, measuring a perimeter or an aera can't tell what are their placement as form in space.
But we need to introduce their forms to be abble to establish their possible relationships. Whyle a quantity is the same type of data under the unit for a perimeter however, for an aera it is defined by the square unit. It is there only formalisms of how to calculate them because a perimeter is a quantity in line and the aera is also a quantity in a line time the one in an another line. Thus, we can use a such transformation to get the final quantity of an object. For example we can define a quantity as a:
[line n time another-line)
It concerns a Quantity definition but not a Form.
It is why the xn formalism induces error to mathematicians when they understand there at first as some Form manipulations. We know it in this next example:
xn + yn = zn
Where one tempts to see there as Three or more Dimensions of Forms.

- el + inventor + de + pi + 3.1416 (Mexico)

It was the Great Archimedes' work. Here proved...

- who + invented + the + mathematic + pie + circumference (USA)

... An anciant famous unknown cordon bleu cook.

- longest + pi + value (Philippines)

how + was + the + value + of + pi + derived ?

- It + is + said + that + the + dimensions + of + the + Great + Pyramid + of + Giza + are + accurate + multiples + of + Pi, + yet + the + value + of + this + number +( 3.1415....) + was + not + discovered + until + the + time + of + the + Greeks. + How + did + the + pyramid + builders + do + it (, Illinois Institute of Technology, USA)

It is an intersting problem to be clarifyed.
When forming large societies human capacity of building is used for building tools, memoriel and monuments. Human technology capacity began empirically. It can be known any of the elemental form et their practical relationship to be abble to project any building. Thus the circle is one of this usual form.
Without meating no theorical impossibility, the anciant architects can practically measure the circonference of a circle and clisified it as a proportional to its diameter.We may noted that a 5% to 10% of relative error is fine for building practically anything.
But it has no good reason to belieave that the Pyramid dimension is a multiple of the Pi=31.14. It is only a archeologist's hurried opinion. The first basic reason is that nobody know what is the exact Pi value prior having resolve the squaring a circle. Even if one know the true value here is a general statement about such quantity allegation.

Theorem on measurement for quantities comparison:
With (x%) of any relative measurement M,
any quantity [nM±(M.x%)] is necessary a multiple of (L.x%)

Where (n) is an integer.

The error of Pi=3.14 is 0.1%. Thus:
(3.14)(0.1) = 0.314

(10)(3.14) ± 0.314 = 9.9 and 10.1
And may considered as (10.Pi)
The result is that 31.4 is multiple 10 of 3.14.

This is more an illusion when M is a great number relative to the measurement error.

It is why an ant can assert that any celestial dimension is a multiple of the ant length!

Rationally tell, this problem is only the Congruence of quantities relative to a unit one.

- he + defined + the + value + of + pi + used + to + find + the + perimeter + and + "area" + of + circles (USA)

That is to say "to put the cart before the horse". Instead of trying to figure out from the circle the factor Pi as one does it when drawing milk from an udder.

- largest + value + of + pi + generated (UK)

- end + of + pi + calculate + finite (USA)

Of what Pi ? The new one ?

- discovering + the + value + of + pi-polygon-circle (South Africa)

- pi + to + 77 + billion + decimal + places (Canada)
A record but... only ???

- science + without + conscience + equal + death (USA)

- past + value + calculator (Canada) - empirical + formula + cheats

- Archimedes + struggle (Canada)

- transcendental + squaring + circle + cannot + be + done

- tortoises + systematic + errors (UK)

Nobody can't touch them. It is why tortoises are famous for their long life time...

- What + is + the + origin + of + the + expression : to + be + beside + oneself (USA)

- robot humen (UK)

- Archimedes + pi + trapping (USA)

- anciant + relationships (Israel)

- How + did + Archimedes + compute + the + "area" (Singapore)

Actually, when knowing only linear form "area"s it is an obvious temptation to equalize a curve with a straight line. The case is for the polygone and the circle. But it is more practical to divide the circle with rectangular surfaces. Such are the modern Algebraic integral calculus algorithms. More quickly, one can do it with pennies or with other elemental tiny surfaces. And really, the result are necessary biased by practical manipulations and also with systematic errors. The quite invisible systematic error is to ignore that it comes mostly from two different space structures as curvatures and straight lines. Therefore, polygons or rectangular convergent forms can never be precisely a circle. Consequently, errors is surely the destiny of integral an differential calculus. In recurrence, any Algebraic convergences and function developments know a such fate. Not only for mathematics, all the modern Physics are quite produced with integral and differential calculus. Unfortunately, it is the Continuum World fate.

- what + does + dividence + mean (USA)

- how + to + loss + weight + without + exercing (USA)

- how + to + work + out + the + "area" + of + a + circle + with + the + circumfernece (UK)

- calculate + measurement + "hight" + tan (Canada)

- How + to + invent + a + formula + that + can + guess + any + number + somebody + thinks + of (USA)

- Archimedes + determination + of + circular + "area" (Canada)

- demonstrate + experimental + methods + of + determining + the + value + of + pi (USA)

- maths +-+ pi ++ 1.34 (UK)

Really a 3.14 of 1.34 Pi. An uncertainty... plus an exact digit permutation.

The Pi value can not be obtained from polygons convergences, even if it was tell that Archimedes had do it. No sufficient precicion can be get from this process. The most probable origin of the 3.1416 old value may come from the empirical estimation of a circle surface. Then, it consists with the obtained value to divide it by the radius squared. For example, with this process, a circle surface [S] computed by digital integral calculus of 1.34% precision, one can get the following result :

Pi = [S]/(radius^2) = 3 . 14 15 927 053

- mystery + of + pi + 1.34 (Hongkong)

- Proof + of + pi + value + as + 3.14 (Papua New Guinea)

- history + of + pi + 1.34 (New Zealand)

The uncertainty value of 1.34% corresponds to a manual precision of experimental measurements. With experimental measurements one obtains always the rounded value 3.1416 of Pi. Note that the Pi value can be derived from the direct measure of the circle perimeter.

- 3.1415 + longest (Argentina)

- empirical + formula + generator (USA)

- pi + 3.1416 + et + son + explication (Canada)

- pourquoi + en + science + physique + on + met + un + seul + rang + après + la + virgule (France)

- conservation + in + measurement + lenght (Malaysia)

This is a quite juste and precise remark.
Thus the following method of measuring the circle perimeter doesn't fulfil the Conservation of length or matter space. The default here is that a circular line is refered one to one point to a straigth length (CD). It is only an empirical view and isn't a vaiable valid method.

- "vaiable" + of + relationship + in + math + field (USA)

- pi cake (Egypt)

- longest + pi + value (USA)

- longest + pi + value (Australia Victoria)

- longest + value + of + pi (University of Nevada, USA)

- How + accurate + was + archimedes + on + pi + compared + to + value + known + today (, Australia)

- Mystic + pi! (

Sciences was born and is colored with Magy.

- most inaccurate value of pi (Australia)

Here is how it is used to do an integtal calculus that seems to be precise. From that one produce a dummy Pi value of 3.1415...

It will be used the altitude AB of a point on the circle relative to its diameter CD. AB is the geometric mean of the blue rectangle surface. The proof is easy to establish. Using the square diagonal CF as proportion transposition, on get directly :

Intégral calculus of circle surface for Pi
The circle surface of (C) is obtained with the summation of all the AB segments when it sweeps the entire surface of (C).
We have :
For the purpose let (dx) a little variation of the lenght BD when it varies from zero to CD. The surface integral is then :

S = Sum from 0 to CD of
[Square root2 of (BD.DE) ].dx
The total circle surface of (C) is then S = 2S

Using the theorical "area" of circle, we get
It give the value of PI = 3.1415...

Doing it with a calculator, here is the algorithm:

Let (dx)= 0.0001
BD = BD + dx;
S = 2 * Sum [square root2 (BD).(CD-BD)*(dx)]
Loop until BD = CD;
The following lines are convention of programmation language type.

Let : (dx)= 0.0001;
Do :
S = S + 2 * [(BD).(CD-BD)*(dx)];
Loop from "Do" until BD = CD;
Obtaining the circle surface S the Pi value is then :
Pi=S/[CD2/4]= 3.1415...

The more (dx) is tiny the more is the Pi value the one given in standard Pi used in calculator. However, with (dx) = 0.001 the precision is sufficient for usual uses.

Example, when the diameter CD=100, is divided into little parts d(x) for surface summation, one get the experimental Pi values as :
(dx)=1;   Pi= 3.1383...
(dx)=0.05; Pi= 3.141555...
(dx)=0.02; Pi= 3.141583...
(dx)=0.01; Pi= 3.141589...
(dx)=0.001; Pi= 3.141592549...
(dx)=0.0001; Pi= 3.141592651...

It is clear that dividing the diameter CD into 20 times is practically easy (case of d(x)=0.05). Even in this case, a summation of the circle surface give also a round number of :
Pi = 3.1416.

With (dx) varying from (dx)=1 one get Pi=3.3836
But at higher (dx) the integral is no more valid.
One can see that empirical Pi values that was given in the whole anciant word can be sitiated there.

- Canada + calculated + complete + pi+3.14 (UK)

- Arabic geometry Archimedes theorems (Japan)

- Approximation von pi nach Descartes (, Germany)

I'm sory to tell it, because in science the space means Nothingness then, Mathematics ignore the space properties as composed by linear and circular mode, the two independent space characteristics.
So, Descartes and any mathematician ignore what is "geometric" construction. The Descartes isoperimeter method is using linear convergence only for convergence towards any given defined value. It is not a rational means to get into the Circular Realm, the unknown point of circle from where a true circle radius can be defined

And more, it is like to, it seems, it hopes, but:
The Descartes' so called isoperimeter method is not a geometric construction!
A geometric construction should begin with straigth edge and compass tools. And also, it should ended with only compass and straigth edge tools. A point in a space structure should be the representative solution.
The so called Descartes' method is only a graphic that is usually shown in science. A graphic is a chart but is not a Geometric construction. Graphic are only shematic diagram as brief language replacing discours.
It is why the socalled Descartes' Pi aproximation is not a geometric resolution of problem. It is why Descartes used algebraic notation to defined the Pi approximation according to recurence mode.
Also, Descartes can't but use the Archimède pi to apply the calculation.
the Descartes "isoperimeter" is only an another mathematician trick of do-it-yourself to paraphrase the Archimedes' pi.

This above Dakhiometry's exercise of calculus for the approximative Pi, is not a paraphrase of Archimedes' Pi. But it is not also a geometric construction because it uses algebraic notations to define and simulate the approximative Archimedes' Pi determination.

Consequence on numeration

- a + linearly + dependent + set + can + be + extended + and + it + will + stay + lineary + dependent (South Africa)

- Archimedes + principle + continuum (USA)

The above empirical method is a general fact in Algebra. Il is most important to know that this process is only coherent in a linear world where there is only straight lines. It is the case of the Geoemtry. But unluckily, it is the basic use of Algebra. There, one uses it to make trips toward the two Infinities and there, to drive any number out of ambush. Infiniresimals and function development series rest on such process.
Thus, with :
(dx) = 10-n
and with (n) as any integer of the natural series, one make decimals. With (n) as greatest as wanted, infinitesimals are produced. And as (n) is unbounded... one discover irrational numbers. Note that irrational number can never be discovered because one can never find it ! It is the great properties of modern Algebra which is so happy to find a base in the Pythagoras' uncommensurable diagonal !
The error of such foundation is :
One cannot belive that the goodness of an imprecise or untouched number is still indefinitly waiting that someone tries to converge towards it. It is a hopeless PRECISION definition that should not belong to just mathematics.

The selfisness is to clame Algebra as a new scientific religion and thus, make mathematics coagulated. While it suffices to notice that one uses these empirical methods temporary until new advance mathematics discover more precise process of numeration. In this case, all the world is informed and mathematics researches will progress more rapidly.

- Absolute + defined + space (, Canada)

Exactly. Space is a concrete absolute matter of perfectly defined location. We should make acquaintance with a such reality to be abble to build a true science done with the human capacity of deduction method.
When the fundamental basis of matter are well established then deduction thinking can do any trip throughout any space structure. Therefore, it is easy to follows any universal law characteristics that are possible only on the absolute universe defined space.

Trigonometric errors

- what + are + the + rules + in + significant + figures + for + foundamental + operation (VietNam)

For the Dakhiometry, the problem of angle measurement is completly defined.
There is nothing to do with the quite empirical manners of Analytical and Algebraic trciks to give the illusion of the current high science exactness. There is no way to get into the exact science until one stays in the ignorance of what is the fondamental universe Space.
The proof is to ask yourself, how on can construct the figure of any given angle value without using the blindness of the Number illusion.
This is to tell that it is a big error to belive that the linearity of Number can't never give a sight in the space angle realm.
It is clear that the squaring-a-circle has no meaning for the current official science.
Because the how to have an access of any spatial angle is necessarily the way of understanding the squaring a circle. For example, from millenaries, the squaring-a-circle is for Archimedes the understanding of how to square-a-square! It is also for the Analytic Geometry inventor, the Trigonometry is only tricks of a recipe book, the way to overlap linear realm on to the unknown of the circular one.
In Dakhiometry the space directions and the measurement of angle between directions, consists of how to figure out the relationship between these two fundamental characteristic of a real concrete and absolute Space.
The so-called precision of trigonometry, scince the numercal capacity of calculators is only an illusion. And the decimal founded for the Archimedes' Pi is the capacity of modern science to catch at shadows.
Without using such tangible knowledge of the matter space, there will be severely no exact science.

Important note
There is no sinusoidal curve in the nature of universal laws, as is learned in the Current Trigonometry.
Even with the spatial circle construction of the Dakhiometry, it is completly proved by construction that the angular function of a circle is a real parabolic curve. Therefore, the Trigonometry is not only an approximative tool but an error of Mathematics resulting in a false angle measurement using Analytic Geometry. It is used in quite all Mathematics for precise applications particularly in Astronomy where tiny angles are very far below the Trigonometric systematic error.
What is behind the Trigonometry?
To be abble to have something for Mathematics to use angle, one had to chose the sides of a rectangular triangle for defining angles. A such choice is no more than empirical action because the space properties are not known in Mathematics.
We can see there that only empirical basis is the foundation of Mathematics. From a such erroneous choice it is not forbiden to Mathematics to build a great realm with the Trigonometry from there modern science and technology rest. The trigonometry is not a particular exemple of modern science capacity to take a wrong way. One can see an another big virtual science with the great Relativity theories and all its derivative results produced in Astronomy.

- Mia + said + that + if + you + know + the + sine + value + of + each + acute + angle + then + you + can + find + any + trigonometric + function + value + of + an + angle + of + any + measure. (, New York s, USA)

That is to say
Azimuthal angle measurements is known when angle between zero and 90 degrees are known, according to circle symmetry. However, how to known what is a given angle aside the multiple ones of 30 degrees.

- Trigonométrie + pour + les + stupides (Canada)

The generation of curvature into the straigth line and inversely, are not simply jokes. Here above is shown how Archimede is in error because he believed that polygon straigth lines can be superimposed on a curvature. Here in the following how can one figures out the distorsion when one tries to use Trigonometry for describing circular lines. It is the case of the usual wellknown
y=R.sin(wt) linear function.

- What does a linear function look like when it is represented symbolically (USA)

- trigonometry jokes (, USA)

- The unbounding function and the bounding function of the progressive construction can (, Egypt)

- what does a quart function look like (, Texas, USA)
- squareroot trigonometric function absolute value (, El Camino College in Torrance, California, USA)

- trigonometry illusions (Philippines,

- railway extends a horizontal distance, trigonometry (, Venezuela)

- trig functions real life (Pennsylvania, USA)

- trigonometry difficult for university (Vietnam)

- trigonometry circle + pi (Thailand,

- organizational structure of RMIT Melbourne university library (Vietnam,

- TRIGONOMETRY HISTORY (, New South Walles, Australia)

- trigonometry animation (Azerbaidjan)

- Sydney opera house trigonometry (Australia)

- Trigonometri (Thailand, =

- lrc linear responsibility chat (Vietnam, linear_responsibility_chart.jpg)

- Sydney opera house cad (Technische Universiteit, Eindhoven, Netherland)

- impossible trigonometri (, Mack, Norway)

- new university in Vietnam (Singapore, university-of-auckland-in-new-zealand-by-fjmt-and-archimedia-drew-4.jpg)

- non rectangular trigonometry (Philippines,

- pastulation (Philippines)

- pictures related to the history of trigonometry (Philippines, 2008/05/righttri2.png)

- The + sine + waves + are + natuarlly + generated + and + it + can + easily + reproduced + manually. + Other + hand, + the + square + waves + are + not + produced + naturally + and. + The + square + waves + require + a + set + of + sine + waves + which + overlapped + each + other.

May be it is only an illusion from drawing where it is easy to represent a square wawe.
This latter is NEVER practically represented by any techniques. Because a Wave is a TIME FUNCTION. Nobody, knows and could practically represent true Square Wave, because there is always some "pico-seconds" duration lower limit limit where a straight Square transition is impossible.

Even with the Fourrier and equivalent methods, a summation of harmonic waves can never represent a Direct precise strsaight line transition.

It is because the Trigonometry is really an approximative Linear method to try representing a Curvilinear phenomenon. The Angular should be from the knowledge of Curviliear property.

It is why a so-called sinusoidal wave is in fact a True Parabolic time-function. This parabolic form is proved in Dakhiometry. The parabolic wave function is directly from NATURAL phenomenon. It is not the artificial sinusoidal Trigonometric form where this latter is only a bad definition according to the Linear Trigonometry. The parabolic form is the true CURVILINEAR Time-fonction of wave that rests on the well precise definition of a Circular Angular Cycle. A curviliear is a true natural analogic process. Thus, the Fourrier method is only from an approximative concept on waves.

Remind that according to the universe fulness of discrete-matters, natural phenomena happens stricly under Universal Analogical Laws forms. It is why the Irrationl Numbers ideas are no more than man's imaginary contradictions.

Trigonometric errors

- imagenes + de + trigonometry + universal (Mexico)

The sinus function is really a parabolic one. It is proved clearly and symply by spatial construction in Dakhiometry.
The Trigonometric Sinus function is due to the erroneous false definition of angle. The total angle of a circle is not for example neither Two-time the 180° nor Two-time the Pi value. It is because angle of a whole circle is Two-time 90° and One of Pi.

It not simply a numerical manipulation but basically from spatial structure.

- trigonometry jokes (, UK)

- trigonometry in equilibrium (The University of Nottingham, UK)

The trigonometric functions can be used to approximatly describe a particular mechanical motion of a disk. It is incorrect to use them as model for general natural phenomenan for example to describe a violon string.

- Abcisse + sampling + cooks (Germany, Vetter-Pharma)

- Fourier (Denmark, AALBORG Universitet, Dep. of Computer Scie home at Cassiopeia)

This figure illustrates the difference between an usual sinusoidal function and the TRUE relation ship between circular and starigth lines. The thick drawing line in red is the true relationship using circular into straight line transformations according to the space constant (pi/4). While in green, localised by a green grid is related to the y=R.sin(wt).
Thus one can see that the true relationship is more uniform in the middle of the curve and for the Trigonometric function the curve more round passing outside of the red curve.

Trigonometry starts to build ratios giving the sine and the cosine from a point on the circle. It is always a true result. However, when apply in Trigonometric determination, one can't but use a linear relation as the y=R.sin(wt). The linearity comme from the time variable. It is there the Basic Trigonometric construction error.

The difference of the Trigonometric function results by an introduction of high energy frequencies. As Trigonometry is wholy used in sciences, it can produce great undefined errors. Particularly when one use signal processing with the Fourier, Laplace and other equivalent equation. Thus in Astronomy, where processing signal are highly used we may get mostly fantasy images to describe the cosmos.

On the figure it appears in a fine red line the derivative of the (S) curve. The derivatived curve is splitted in its phase for a better comparison of their slopes. This forme shows that a derivative of a true circular cycle function fonction is not a Trigonometric (sin) form equal to a (cos) one. Therefore, in a Fourier sommation of signal harmonics their successive derivatives introduce necessarry both Low and High frequencies. For example, for an initial visible light radius after signal processing one will see there very much amplified Red and Violet light signals.

Looking at the first derivative on this figure, it appears that in some derivative degrees the signal (S) will look like to a square signal. That is for a visible light a Fast Fourier Transform in signal processing can produce only a major Red light where the high frequency parts are there becoming invisible light.

- pi + harmonic + "fonction" (Syria)

Dakhiometry example of True formula for
Space Directions mesurements.

- trigonometric construction (Korea, EZ International Patent & Trademark Law Office)

- Application of trigonometric function (India, Railnet GOV)

In Diakhometry, measurements of Angles are really determined at least on its basis. Developpement of this method may be more and more in enhanced fertility by futur generations. True knowledge of space will be therefore unbounded science.

- Geometry and Trigonometrie (South Africa)

- curvilinear function (USA, Pennsylvania Lehigh edu)

This next example of angle sine-cosine definition is really a continuous curvilinear Direction variation.
The Tigonometry of angle is only a linear approximation of angle variation around a central point. Because the sine and cosine are linear segments that can't produce a true correspondence of one-to-one point with the circular line.
The following example use Algebraic number notations is not the ideal function form. There is in fact a real complex space structure that is the true source of a fertile space directions knowledge. But it can't be understood easily without knowing how to spatially construct the addition, subtraction, multiplication and division operations.

- rectangular + triangle + relations + between + trigonometry + formulas (Estonia)

La Trigonométrie avait été montée seulement comme moyen nécessaire pour les angles. Mais les Mathématiques ne connaît que le monde référé par des axes linéaires de la géométrie analytique. C'est pourquoi la Trigonométrie porte le défaut de manquer de continuité dans sa génération de la continuité des angles autour d'un point central. Ceci, parce qu'avec une variable (x) comme abcisse sur une ligne, il est impossible de générer la continuité d'un cercle. Alors, la Trigonométrie ne peut dessiner un cercle qu'avec plein de trous. Dans ce cas, l'espace des directions, reste toujours incomplète. On ne le sait pas, simplement parce que les Marhématiques ignorent la différence entre le Linéaire et le Circulaire.
La Dakhiométrie, ayant réalisée la quadrature du cercle et inversement, connaît l'espace des Directions, c'est-à-dire comment déterminer les angles avec précision, par la Règle et le Compas.
Ce n'est pas facile de l'exposer parce que c'est un monde NOUVEAU inaccessible aux optiques Mathématiques, par ses ignorances et particulièrement, par orgueil et suffisance millénaires.

Je vais vous donner ici un court échantillon pratique, sous forme algébrique compréhensible par vos formations mathématiques. Vous le comprendrez le mieux, sans les préjugés mathématiques sur les Nombres. Entrez dans un monde encore vierge des pollutions mentaux. Faites taire vos savantissimes formatages mathématiques alors, sans doute vous seriez prêts à être vraiment savants!

- sinusoidal finesse (Turkey, Ankara Bilkent University)

This next relation is a function of infinitesimal variable values (n)=dx.
Starting at one (dx) to describe a 90 ° we can see that at lower angular values less than 5°, there are not continuity in the circle function. That is to say, there is no continuity when number are used even infinitesimal are used. In Trogonometry, where the linear coordinates are {y,x}, the circle perimeter continuity at lowest sinus and cosinus are nescesarrily bad.
Therefore, what do we conclude for Astronomy where very low angles are measured?...

- formule mathematiques du big bang (, USA)

Vous l'avez bien vu.
Pour vous dire que cette formule si simple, est à la base de la représentation des Quantités de l'univers. Il ne s'agit pas de la série usuelle des Nombres mais, de la représentation complète des Quantité de l'univers. C'est une représentation de quantité par des rapports de longueurs.

Il y a une représentation des Quantités de cette manière mais, selon le mode Linéaire, qui nous est plus facile à comprendre, puisque la connaissance commune des Mathématiciens est de ne connaître et d'apprendre que selon des représentations linéaires.

Mais, le merveille des merveilles, est nécessairement la représentation selon son origine qui est de le faire dans le mode circulaire. C'est-à-dire à l'aide d'une structure de cercle.

C'est facile à les dire mais, le chemin pour y semer la clarté est si long et si diifficile, non pas en elle-même mais, parce que les mathématiciens ne connaissent que ce qu'ils avaient appris et ce qu'ils enseignent, toujours dans la rigidité morte du linéaire.

Mais en vérité, une telle représentation de toutes les Quantités de l'univers par un cercle est un autre veritable Big Bang. Car, il faut gravir notre robotisme et automatisme, une montagne certainement plus haute que celle de Mars, une montagne comme celle de la Terre en Carré, un relief à côté duquel la Séries Infinie des objets imaginaires de Dedekind, n'est qu'une platitude d'un terrain de tennis tout neuf.

Voici une idée de comment générer les angles, si l'on ne sait qu'utiliser le vieil langage des Nombres:

Mesure des angles en Dalhiométrie

Mesure des angles en Dalhiométrie

Cette formule génère, à la fois, le sinus et le cosinus du complément, des angles de 90° à 0°, rien que cela,
par exemple, de mesures d'angle en degré.
- Avec la vaiable (n) qui est un chiffre variant de Zéro au Sans-limite, en quantités continues de la matière discrète. Il suffit de renormaliser les variables pour obtenir les mêmes égalités classiques de la Trigonométrie.

Faites en la vérification, cette formule donnera la continuité de tous les angles d'un quadrant de cercle, allant de 90-0° pour n variant de toutes les valeurs décimales possibles.

Evidemment, la racine Zéro-ième est une erreur de calcul. Simplement cela est dû aux méthodes algébriques de calcul des racines, par tâtonnement en exhaustion de divisions.

Mais cette formule simple, permet de calculer à la fois, tous les arc-sinus et arc-cosinus. Comme simplicité de la Dakhiométrie, il n'y a pas mieux!!!

Elle donne directement le sinus et cosinus de tout angle dans le quart de cercle directionnel de l'espace. Avec l'Arc-cos on obtient la valeur de l'angle selon l'unité choisie.

Cette fonction génère la continuité des angles de l'espace. Cependant qu'avec les moyens Algébriques, il y aura toujours des tous de valeurs, dus à la non-continuité des Nombres Algébriques. Les calculs utilisés pour vérifier cette formules se font avec les modes appliqués de Trigonométrie, inclus dans les calculateurs. Les angles générés par cette formule souffriront des défauts des méthodes de la Trigonométrie.

Dans sa vérité, la définitions par mesures des angles, ne sera qu'une merveille que par l'espression des constructions par l'espace. On peut alors avoir une vue d'ensemble d'une structure complexe qui donne une vue complète des angles. C'est de cette structure que cette formule algébrique ci-dessus est tirée.
La Dakhiométrie est à même de montrer la haute valeur du véritable Penser humain.
Ainsi, lorsque je disais que les Mathématiques et la Physiques des sciences en cours ne raccontent que des bobards simplistes de primitifs, ce n'est pas parce ce que "j'aime ou j'aime pas ceci ou celà". Les sciences en cours ne sont que des fantaisies de "savants". Ce n'est que des paroles du Penser rationnel que chaque homme est encore incapable de deviner sa propre capacité... mais malheureusement bien momifiée et plein de suffisance.

- cosine + law + prove + concrete (Canada, Alberta Edmonton)

- examples of real life square root function (USA, Florida)

- computer resolution circle drawing (Korea)

- big crunch diagram (Columbia)

- GALAXY creative Vietnam (Singapore)

- weird science animated (USA, New Jersey)

- equation describing a circle (UK, NHS Health)

This equation can describe a circle continuously. Continuity here depend to the division algorithm of modern calculator But is more fine than the usual Trigonometric sine and cosine in an orthogonal co-ordinates reference axis.

- prove + the + existence + and + uniqueness + of + a + perpendicular + drawn + from + a + point + P + to + a + line + L (USA, New York, Poughkeepsie Marist College)

Uniqueness of a perpendicular to a line L, is directly from the structure of a rectangular triangle inscribed in a circle. The two rectangular sides of this triangle are unique lines defined by a circle.
In addition, the above formula of angle sine-cosine show that any angle is uniquely define by a circle. Therefore, a perpendicular from a point to a line, is necessarry unique according to that any angle non rectangular in a rectangular triangle are unique.

The usual angle functions determined by the Dakhiometry

- use of trigonometry in daily life (India)

- transformation from circle to angular (Singapore)

However, it is only because angular quantities are directly the circle property. Contrary to the Trigonometry that introduce errors in the angle definition when it is done according to the linear Analytic Geometry axis.

- different symbol use in trigo (Thailand)

It is here shown under particular formalism. But when expressed un full spatial language, this latter is an fertile enlightening on the precise angle characteristics.

- thales trigonometry (Australia)

These are only formalism resemblances. One can see it only when they are expressed in pure spatial language.
If a such trigonometry can be built with the Thales rules, all of the world mathematicians of the anciant times probably had done yet a such system.
There is really a more basic reason that allowss to get a so fertile view point.

- Importance + of + having + the + basic + knowledge + in + trogonometry + to + the + college + students (, Philippines)

This following formulas are the basic ones for angle determination. They are very fertile and easy in applications. When calculation with spatial elements is applied with them then, the precise angle properties can be unfolded by deduction in extended wealthy space structure.

- why + do + all + the + angles + in + a + trinagle + add + up + to + 180 (, Eastern Illinois University, USA)

It is a basic remark.
Now that the angles are determined by a point (A) on a segment (BD) then the answer will be more precise. A triangle is only a brief of a circle circumference. The total triangle angles is only situated between 0-180 degrees because the circle angles are completly determined by the point (A) in (BD) can situated only between (BA=0) to (BA=BD). It can varies back between (BA=BD to (BA=0). This is a form of angle variation stricly between (90.2=180) degrees
Because the linear is born from the circular then, the basic reason is from a fixed point, two intersecting lines can be never more than being perpendicular and make an angle no more greater than (90.2=180) degrees. We should note that the perpendicular line is then the property of circle angle. A Triangle can't have no other angle property than the circle one.

- nature + of + mathematics + "pastulates" (, India)

At least a great pastulate...

The Dakhiometry had proved and spatialy constructed all the functions to determined completly the basic angles between 0 and 90°. These proofs rest on the basic properties of the absolute space the ones unknown in Mathematics.

The angle determinations are as follows:
Let any determined length (BD).
Define three colinear lengths related with (BD) as:

BA + AD = BD

Circular knowledge consequences.
Fulness of space-direction determination method in Dakhiometry

- the properties of angle in circle (Malaysia)

Actually, only and strictly, circle properties can resolve the space Direction and then, consequently, the linear realm.

You are informed that the Dakhiometry method of dtermining the space Direction - usually denoted in the classical Trigonometry as Angles -. They are done more simply, perfectly precise and with exactness.
Any angles are defined by the above ratio (BA + AD = BD). there is no need of sine and cosine definition and no more their inverse as Arc-sin for example, to expressed them in degrees or in another unit.

For example,
An angle is given as the ratio conventionally named as follows:

         Dakhi-Cosine... etc

And it inverse derivative Arc-cos is directly given by simple spatial construction. This give the direction relatively to a reference one. So let a given angle (a) in any choosen unit, you can figure out precisely a such angle.

Also, from a given angle (a) in degrees for example, it can be simply constructed its form as this above "cos" ratio. That is to tel, with any ratio (BA/BD), one can figure out an angle without calculating the Arcsin or Arccos that are only approxiations. And given any angle, one can determine the ratio (BA/BD) corresponding to this angle.

Any angle value are rationally spatial constructed. and the usual addition-substarction-multiplication-division can be used to transform this give angle.
For example, one can construct any inscribed polygones in circle with any given vertex.

Note on errors in Trigonometry:
The current Trigonomety can do better angle definitions than with with 2% error. It is because of the Archimedes' Pi systematic error that is no more precise than to the first decimal.

How can Astronomy and Cosmology can be built on such hugue errors?

A Universal device for defining
the Directions of the universe Absolute Space

It is informed that
The Dakhiometry Science can conceive a theorical Universal-System for defining with high precision the angle in Three-Dimensions of a Globe.

This means that this system can be use to define any direction in the whole Absolute Space of the universe Globe.

This system may use the modern numeric technology that can drive for a maximal pixel definition. This device can be refered to any fixed defined direction.
Obviously each "E.T." may have his own reference of direction. This is only to tell that eachone on Earth for example may have his own conventional language. One needs only interpreter. Because it is not yet possible to define the ansolute Latitude and Longitude of the universe.

Thus for the Earth one need only to define any given fixe direction as the one for fixed reference.

For more precision of angle measurements,
one don't use no more the old 0-90° or the Achimedes's Pi. For exemple while using 0-90° it can be use the (0-9n)° interval [(n) = any integer)]. Any angle is then define by numerical integer. The angles can be accessed on a whole Globe aera and the Line directions may be realized by Lazer ray type on the basis of the Spatial language. There is no more calculation using the old irrational and imprecise Number systems calulations. It can be read directly from there the Angle and its cos-sin values. These values are not from calculation (the old euclidean division by exhaustion!) but by reading directly from the system structure.

A such system design is only possible with the Dakhiometry Circular KNOWLEDGE construction. The actual Anciant's Trigonometry is simply a scientific spiteful trick that necessarily introduces errors in astronomic measurements.
Note that this is concerning DIRECTION MEASUREMENTS. Because it is false to state that Light Ray property can be used as Distance measurements.

The use of Lazer Rays allows to associate the lazer Ray for practical construction ... as spatial Lines of the Dakhiometry Spatial Language construction.

The Dakhiometry Spatial Language can do any concrete tansformation of space figures by (Add., Sub., Mul. and Div) applyed to spatial and rational method contrary to the old irrational and conventional Numbers of Algebraic systems.

The Spatial Language is the foundation of futur human sciences. Without such knowledge of the concrete Space and its alphabetic tool there is no possible science... but only man's obscure believes.

- comment + démontrer + qu'un + triangle + est + équilatéral + dans + un + rectangle + avec + cercle + circonscrit + au + rectangle (Paris)

En effet,... par symétrie, que CD est égale au rayon de ce cercle.

- equilateral triangle with equal area of a square-construction (India)

Here next is the result.
From this figure the construction understanding is "for Kids".

The way is at first to determine a great green-square the side of which is the one of the equilateral triangle. Then, you start the Lam-Ca theorem that gives the how to construct the correponding square.
Note that to get the square aera equal to the "equilateral-triangle" it suffice to get the square (S) and it corresponding circle with diameter equal to the side of (S). And then to get it half square with the Lam-Ca theorem.

Equilateral aera into a Square one

This figure shows how one can construct the equality of aeras between two different forms. Here is concerning to construct a square aera (S) from the one of an equilateral triangle (ABCD).
Spatial construction is simple to get exactly the result.
Concerning aeras, the Lam-Ca theorem is the top.

One have to archive the Old pytagorean theorem in his big Museum and should rapidly be in acquaintance with this great usefulness Lam-Ca. Any miracle and more are from it.


1) - The current Geometry is as most of existent type of languages as well as the Number-system, belong to the classe of interpreting-language.
For Interpreting-languages the information is given by this language and not by what it seems to represent initially. This mean sthat the information is furnished directly by the language itself.
For example:
(1 duck) represents a-Duck Or a-One,
according to the interpretation of each one.
This is the ambivalence of any Interpreting-Langauge.

2) - While the Dakhiometry Spatial-Language is directly the universe Matter being. The Spatial-Language is a rational scientific language because it is itself the Object-and-its-Meaning or the Object-Meaning

It is why the Spatial-Language is directly the expression of the matter behavior. There is not relativistic meanning depending to eachone particular interpretation. For example:
a Solid rock is a solid rock and not depending to what eachone believes its as an angel or his contrary.
For example about this above equality between the Square-and-the Equilateral triangle aeras, with the Spatial-Language we need not to modify the geometric figure and then searching how to draw what one supposed to be.
Because in Dakhiometry, this problem is to examine the spatial fact in the matter Spatial Structure where it may be inscribed the fact or the anti-fact of a searched equality. One has not to invent the searched relationship and then interpret the result as one had presupposed.

The Dakhiometry Sptial-Language is not an Interpreting-Language. It is why the Dakhiometry Spatial-Language is necessarily the basic tool for advanced rational sciences.

- prouve perpendiculars in triangles meet in one point (

- triangle + in + circle + with + lines (Belgium)

A circle is not really defined as a perimeter around a radius from a center. This is only the usual compass stereotype.
A circle is a succession of points defining the whole space directions the so called Trigonometric-Angles. From this latter, the linear positions of radius around a center are used to define the Trigonometry.

From there Mathematics remains in perpetual ignorance of the circularity. The millenary Squaring the Circle was Impossible because one is tempting to constraint a perimeter to be supperposed to a Straight Line. This is also the case for the mathematic Trisection of an Angle. The Morley equilateral theorem for example, is from this impossible view point.

Why a triangle is always defining a Circle? It is because a triangle is defining the precise points on a Circle and then can directly define the unique 180° corresponding circle. A circle is only a 180 degrees or two half 90 degrees half-circles !

- 180 + degree + circle (..)

Really the circle property is as angle or Direction definitions.
In this view point, the Circle is divided into Two parts by its Diameter. Each half-circle define one half of angles or Directions. Therefore, the whole circle is can define all of the possible angles in the space.

Thus if one choose angle on the basis of 0-90° then a half circle determine 90° of directions.
And a Whole circle is defining all the 90+90 = 180°

On can verify that all the Circle Possible Angles can be defined by all the inscribed Triangle angles WITHOUT REDUNDANCY.

The 360° is only from conventional Trigonometry that rests simply on the artificial Linear orthogonal reference where the space is necessary divided into four quarters. Therefore, 90+90+90+90 = 360°.
The trigonometry ignore what is the basic of Circle.

In the true rational definition of Circle for the Dakhiometry, the angle definition rests on the Half-circle as capability for defining 0-90° angle extend. The high exactness of spatial construction allows to use not only the anciant's 0-90°. But the spatial aLanguage allows the used of 0-90n °.

And obviously also the angle definition with the total angles as equal to Two-Pi, as the Two-Dakhiometry-Pi by spatial construction. Where for example, the angle extend may be half-circle extend as [angle extend = From 0 to 312019372702489... as wholy integers].
This will be used for defining more precisely the astronomic heavenly bodies repartition over the wide universe Globe Space. The definition of the univers globe angle (altitude and azimut) by successive ... one to one definition on 312019372702489 extend. This will be accessed for futur human's science technology. The present theorical basis is a fact.

180 degree circle/triangle Three points of a triangle determine a Circle and inversely three-points of a circle determine a triangle. It is according to that the total angle of a triangle fulfil the the whole total angle of a circle.

From any point it can be drawn perpendicualrs to three sides of a triangle as a circle center can do it to its three chords forming an inscribed triangle.


It is why, the total angle determined by a circle is for example 180° and not the usual 360°. It is because the current Trigonometry rests on the conventinal angle determined from the circle center.

This is not correct because a GIVEN ANGLE in a Circle should be defined by THREE-POINTS LOCATED ON THE CIRCLE PERIMETER and not from the Trigonometric according to circle Center of Linear reference.

On this above figure it can be done the mirror (xx') symetry of the ABC triangle. The result is the same when doing a 90° rotation particular to each separatly sides AB, AC and BC.

It proves that from any point (O), it can be drawn pependiculars to the sides of a triangle because the total angle of a circle is 180°.

It is why the Dakhiometry definition of angles, by spatial constructions, is done NECESSARY on the perimeter of a 90° semi-circle.

The main true characteristics of Circle are matstered in Dakhiometry

Mastering the Circle is to get the clear understanding on the universe isotropic Space. This is the top fundamental knowledge that allows man to get a rational understanding on any of the univers Construction and thus, to perform the optimal action in and for Life.

The mains characteristic of the isotropic space is to get the control of the Circle characteristics as:

I) - The understanding on the Angular properties.

II) - The rational tools for doing the Four Operation on the Angle, by Construction as the addition, the Substarction , the Multiplication and the Division.

For example the old Famous impossibility of resolving the Trisection of an Angle is the fact of the current Mathematics ignorance on the Circular Realm.
This problem is wholy resolved in Dakhiometry for any angle difined in a Circle. That is to tell ANY Particular angle of the whole Circle can be divided by three
and consequently one get directly the trisection result of their complementary one.

This means that the Dakhiometry had defined the rational and precise definition and the measuring for Any Angle of a whole Circle.
And also the true Basic definition of any angle by construction.

It is noted that the current Trigonometry is simply a Linear technique contradictory applyed for defining the circularity of angle.
The usualy known as the Trigonometry is innacurated.

The Trigonometry is an inaccurrate technique when it is applyed for measuring precisely faraway Star Locations particularly when one believes that Light-Ray-Energy indicates the Distance!!!
... Light Ray is from another man's ignorance

Errors are due to that the Mathematics sinus and cosinus functions was usually determined baddly according to Linear reference.

While for measuring angles, the Dakhiometry had defined the optimal true Circular reference corresponding to the angle as characteristic strictly from the circle property. The true varaiation of the sinus and cosinus are exactly done according to parabolic trajectories.
It is noted that the usual mathematics parabolic curves (y=a.x2) is seen only from an orthognal reference. It produce for mathematicians the belief that a parabol is a linear function.
It is there also an error.
Because, it should be seen that the parabol is directly from the circle property. The fact is that the parabol construction is generated AROUND its own Focus !!!

Dakhi-Angular Definition This next diagram is from spatial construction of the Angle characteristic from circle. The curves of angle variations around the circle are get from spatial construction, refered directly from circles. The usual sinus/cosinus are defined refered directly to by the circle and not as it was done in the current Mathematics Trigonometry.
This latter is really only from the primary step of the Mathematics. There the sinus/cosinus are only from a Linear orthogonal axis system. This produces only an approximations of the angle variations.

With the true Spatial Language from where this circular reference is constituted then,
1) - Give an angle value then one can Read directly on this chart the usual angle characteristics as: sin, cos, tg and cotg.
2) - Give any of the angle characteristics then, one can get directly the reading of the angle value.

No nead to search in his memory the listing of the usual Trigonometry cumbersome practical predefined values.

Note that without predefined definitions the Trigonometry remains impotent.
This is from the true spatial language that is not from prdefined artificial memory. The Spatial Language is the direct homothetic representation of the universe space property from where one have only to know how to read it.
This understanding of circular space is the infirmity of the current Trigonometry.

Without the Circle knowledge the base of the Spatial Language there is no possible rational science else than the usual Mathematics presuppositions by axiomatic, postulates, hypothesis and also divination.

The angles may be defined between (for example 0 and 90°) as for the circle quadran (A). And for the whole circle, it suffices only to get the complement (A1) and the supplement (A3) and (A4) from this first quadran (A).

This fondamental circular system for angle definitions is a precise and complete one. Also it is practical because it can give the direct correponding value of any angle from the circular characteristics. There is no need of the usual (Arc-Sinus,...).

The usual angle values of 0-90° was only from the Anciants. This gives the cumbersome decimal values that have no meaning according to that the Trigonometry is only an approximative "do it as you like". It is quite a bad joke to apply these angle vallues for astronomic faraway observations particularly with the Pi = 3.14. The fact is that according to these Trigonometry techniques of angle measurement the precison is no more better than 2%. A 2% of light celerity is rather a big deal...

In the futur according to the high precision of the Spatial Language construction, the angle may be better choosed as for example in the scale (Zero and 9000°) or with more biger values than the simplistic Anciant's (0-90°).

This above shematic of the Dakhiometry is only simple. It have to be more precisely dexcribed on how it should be constructed and how practically exploited it as rational science.

In summary
For the Dakhiometry method,
any true operation by construction on the Angle can be done as one does it for the current Linear figures.

Physical view point, the universe space is a structure of potential circles. Only from there, the circular structure can then be created as Parabolic kinetic energy. The Linear motions are there only particular phenomena. Remind that heavenly bodies are only organized under circular structures.

Here follows are exemples according to the trogonometrc conventions for a best easyer understanding. Then, we can define from there the angular continuity of functions for angle (a) situated between 0-90° as follows:

In the following and due to the angle complementary, a given,

Dakhi-Sine       or       Dakhi-Cosine

can be used to get both the angles as (arc-sinus) and (arc-cos).






Cos a+b


Let (a+b)/2=BA3 and (a-b)/2=BA4 then,
is written as:



- rational + values + of + the + cosinus (, Spain)


- SEEDING SLOPE FORMULA (, Time Warner Cable Beaumont, USA)

- applications of trigonometry story problems (, USA)

It is usually known as Trigonometry however, here is represented a brief introduction to spave Direction determination known as angular measurement. It is quite complete precise definition of angles with its basic tools for angle transformation. Because space Direction is from circular realm quite different from the Linear mode. This latter is only originated from the initial circular mode therefore, the linear can be only some practical approximations with irrationality imprecisions due to Numbers as strictly dichotomic language words.

A complet and precise Angle determination
in Dakhiometry

You are informed that Space direction or Angle is still unkown in Mathematics even if it was created there some apporximation with the empirical Trigonometry.
The Dakhiometry had achieved a complete precise and rational scientific system of defining angle, according to his full knowledge on the space circular realm. Angle is rationally determined according to precise space constructions.
It shows that the Trigonometry has a certainty no better than 1e-6. It is not included there the classical Archimdedes' Pi with its uncertainty at 1/10 of unit ( 3.1??? ). This proof of errors is determined by spacial constructions which is characteristics of absolute precisions.
It is not easy to simply expose it here because a such system need deeper basic space knowledge that mathematicians has no access. It consists to know how to calculate space structures with the space language then, to know how to manipulate the circle and any conics figures. We have to consider that Mathematics Geometry and Analytic Geometry is really simplistic when compare to the Dakhiometry science possibilities.

Important difference:

Trigonometry uses Cosine and Sine for defining angles according to a linear orthogonal axis reference.
While the Dakhiometry Angle definition use direct circular definition of circle arc.
There is no sine and cosine and their derivative conventions.

This allows to use the four transformation operations on circle arcs or angles, as addition, substraction, multiplication and division.

Circular lines are then completly equivalent to linear lines for any space structure construction. For a simple example: it can be done by using space construction, the Angle Trisection and more, to divide an angle by any quantity. Any circular polygon with any integer number sides can be constructed as a circumference divided by a natural Number. Note that this process can't never produce a circle as was tempted by Archimedes.

Such possibilities are one of the most important consequences deduced from the Dakhiometry squaring a circle solution.

Example of errors on some angle measurements
On figure of the squaring a circle it can be get the angle that allows to determine the form transformation.
Let this angle denoted as AS. In the following are measurement differences between trigonometry and Dakhiometry.

Mesure with the classical Trigonometry method as it is used with a CAD sofware this angle is given as:

1) ------------- Trigonometry:
Dakhi-angle ; Dakhi-angle

Dakhi-angle ; Dakhi-angle
With the Pi value 3.1416... of computer:
Dakhi-angle ; Dakhi-angle

2) ------------ Trigonometry:
Dakhi-angle ; Dakhi-angle

Dakhi-angle ; Dakhi-angle
With the Pi value 3.1416... of computer:
Dakhi-angle ; Dakhi-angle

3) ------------ Trigonometry:
Dakhi-angle ; Dakhi-angle

Dakhi-angle ; Dakhi-angle
With the Pi value 3.1416... of computer:
Dakhi-angle ; Dakhi-angle

- trig use in cad ( (West Ottawa Public Schools, Canada)

There are current illusions in modern technology where anything are determined by digital machines. For calculations, one attributes precision with math-coprocessors long word digits. But it is an illusion when the main action is controled by the softwares. These latter are no more than the usual Mathematics algorithms that rest on the approximate circular functions. For exemple the Achimedes' Pi value in conjunction with the current Trigonometry introduce error until 1/10 in any calculation result.

Any of CAD sofware used in the whole word contains the Archimedean Pi (as 3.1415...).
As circle are highly used in practical CAD designs, paid attention that even if math processors used with long floatting digit precision there are many great errors during calculations for figure constructions. It is because most of figure in modern technology concerns circular forms.

The introduce errors ares not visible because every calculation rests on this same incorrect constant. For example if you measure your house with a same false unit of 1.5 meter length, you will not see there any error. However, you need an external another unit of 1 meter length to be abble to see that all your anterior measures are really erroneous ones.

The Pi=31.1415... is a bad value for high precision mechanisms.

All the Dakhiometry calculation are done by space construction and not with the Algebraic operations. It is needed only to divide two lengths then to multiply them by an final length. No classical Trigonometric formula is needed as for example the arc-sine function.

It is noted that measuring the space structure is done also directly with the Space Constant length as:
Space Constant = 3.120 193 73
It is seen that the old Archimedes Pi introduces error until the unit angle.

Measurement Conclusion:
Measurements on figure lines are more precise with a minimum use of digital number calculations. Therefore the result with the Dakhiometry method is better than the uncertainty of the Trogonometry plus the numerous step for calculation using particularly the Euclidean division.

Therefore, the errors from Trogonometry is seen there with no better than 1/1000 decimal. This can be obviously worse ones when theses errors are repeeted during a long algorithm repetition of initial errors.
Trigonometric angles are not as exactness warranted from second of angle precision or les than 1% degree precision.

Science errors are the most serious modern problem that international human society has to rapidly resolve. Nothing can't goes further in optimal evolution ways when it rests on false actions.

- application of trigonometry (, India)

- trigonometric proofs (, TampaBay DSL, USA)

What are shown here are only first sight. The Dakhiometry circular angle definitions are complete. Angle can be manipulate for precise transformations as it can be done in linear mode.

Sailors use to search their displacement direction according to stars with the sextant navigation instrument. This latter rests on a three axis coordinates principle. This is a method irrelevent in three dimensions extraterrestrial space because there is no terrestrial horizontal as given plane reference.
For the Dakhiometry method of spatial angle determination, it needs no more the sextant principle. It suffices to determine the direction target relatively to any fixe given reference direction. For example this latter is determined by a faraway star that can give a sufficient good direction of reference. It is considered there that the parallax of a faraway star is equivalent to a fixed direction. Then the linear straight way toward the target is known.

All the trigonometric formulas can be easily verifyed with these above equalities.
For example, the (cos 2a) can be extended in its general form as
(cos n.a)
It is impossible in Trigonometry to express a such relationship because of its formalism complication. But in Dakhiometry, a simple spatial structure can define the multiplication of an angle (a) construction. Its allows to construct a polygone in a circle without worying with the successive reporting of a same arc or chord.

Note also that in Dakhiométrie all the four basic operations can be done on the sine and cosine, for example:

(cos a)/(cos b)

is easily done. It suffice to read the result from the space structure. The continuity of the sine and cosine should be done with these relationships and not with the angular velocity as (w.t).

Spatial Direction in three dimensions

- cosine curve in three dimensions (USA)

Angle is the space characteristic of Direction.
From there any angle in three dimensions is determined by this above formula even if it is given here only a shematic formula of the Dakhiometry for angle determination.
Therefore, any angle is determined from one given space direction as a fixed referent angle direction. It is the BD direction as referent. A space direction is a straight line direction. It is the case of a spatial vessel standing at a given absolute position point (B). From there it can go toward any other given direction according to the above angle formula from relationship (BA+AD=BD).
Now obviously it can be defined any direction 3D space, by choosing two or many other different determined directions as referents ones.
To go a distance at any precise point (D) it must be known precisely the distance (BD).

Basic tool to define an agnle

- trigonometry basics descent (USA)

Here, space direction rests in steady deep basic sources of space properties. It is more precisely, clearly and completly defined in spatial language. Angles are there defined not with linear Numbers but by spatial elements of discrete space. That is, angular directions are defined as space points seen from a given fixed point.

Angle can be only defined by circular manner. However, we human can only have access to linear capbility. As in Analytic Geometry, angle is erroneously defines by two coordinates of orhtogonal lines, named as sine and cosine.

The Dakhiometry can spatially prove that the circular angle can be represented in using relationships between three colinear line segments as:
BA + AD = BD
In this case Any angle (a), for example between 0-90°, can be define by a length (BM). This latter is used to figure out the particular angle (a) by the spatial language forms. It is written as the following:

Angle (a) = BM = sqr(BA.BD)

The curve as a result, is seen in this next figure, comparing to the usual Trigonometric function:

y = x . sin(wt); or with cos(wt)

In Dakhiometry, the "angle=(BM)" is not a function of a so called angle variation but is a quadratic function of the segment (BA). The curve is denoted by (1) relatively to the (2) one of the usual Trigonometric function.

We can see on this figure that there is a real difference of the quadratic function with the linear Trigonometric formalism.
The (BM) is on the Y axis while the variable (BA) is on the X axis.

- sound in parabole (Cyprus)

Sound is necessarily due to movement in parabola form. Also it is for any vibration in nature.
The reason is the universal law of absolute space where potential energy governs the space location of any object. A potential is composed of a defined rest point location. Kinetic energy is then the consequence of potential location from where material object cyclic changes around its rest point. This is the universal characteristic of absolute location in space.
Then sound is material atomic and molecular matter that move around their local rest point and also of system of these elements that is orbiting around their rest point according to the potential versus kinetic energy law. One should consider that heavenly bodies orbiting not in perfect circular orbits are also vibration whith ultra low frequency. For the earth for example, the cycle is one year duration. But we can consider that these duration is no more the vibration scale and be considered as movement one. Heavenly bodies remains in conservation energy because they are independnent object by matter condensation process constructions. Thus, the Newton Universal Gravitation is a contradiction where a Big Bang and a Big Crunch principles are contradictory to the Energy Conservation in the Whole universe. An absolute space has no expanding nor crunching mechanism and the Relativity in space is only anthropomorphic empirism of historic bad tale.

- sine wawe to square wave converter (Latvia)

A such electronic instrument is consistent with the sound phenomena. A loud-speaker is really functionning according to such function. Probably the speaker working will less suffer the resonant and distortion effects than with the classic mode of the Trigonometric sine function produced by current synthesizers.

- Algebra and Trigonometry jokes (, Saratoga Springs City School District, New York, USA)

Really they do. Because there is a precise approach of definition when using the properties of space. The element of space language can do it with an easy understanding of problems when space strutures allows to defined their curvilinear an the linear aspects.

- creative sine function (, Brookdale, The County College of Monmouth, Lincroft, New Jersey, USA)

- trigonometry on curved surfaces (Korea)

- Sydney Opera house hyperbolic paraboloid (Ireland)

- what does a convergent function look like (, Canada)

- trigonometry comparison (Indonesia,

- parabolic trigonometry (, California, USA)

- fungsi grafik trigonometri cosinus (Indonesia)

- how + does + Trigonometric + form + of + a + complex + number + apply + to +daily +life (, USA)

- trigonometry in medical image (USA)

Modern surgery using computer 3-dimensions images aid needs not only exactness but precise point determination e.g. is the brain surgical operation. Precise 3D directions is there needed.

- vision the library university RMIT (Vietnam,

- grafik trigonometri sin 2x (Inonesia, period-sine-cosine/images/)

- closed form expression acos(wt) (, University of Strathclyde, Glashow, Scotland, UK)

- Egypt quadratic function (Malaysia, commons/thumb/d/d1/Quadratic_equation_coefficients.png/)

- linear + responsibility + chart + example (

Actually. The current Trigonometry was built on the Linear (x;y) orthogonal reference.
This may be considered as a good approximation for angles situated between 10/80 °. For low sinus and cosinus there are too much deviation from the precise true angle. This concerns for astronomer where faraway stars forms have to be measured with very low decimal angles. With the Dakhiometry, it is proved by construction that the wellknown sinusoid curve is no more than a True exact parabolic function.

This Trigonometry discrepancy is due to that from millenary Mathematics really ignores how to define a Circle. The squaring a circle impossibilité proved that the circle is actually ignored in Mathematics. The Platoo's Compass is an illusion for defining a Circle. It is because in the Anciant's time, Geometry was formed practically on Mechanisms analogy. The Platoo's compass is a simple passive mechanism.

When was know rationally what are the circular properties then one can define what is really an angle. Because angle is strictly the property of a circle. An angle can be precisely defined when one can defined a precise two-points on a circle. When a language composed with spatial elements is known and used un science than Excact Science can be built because any form in space is necessary derived from the Circle knowledge. The Circle property is a Gate for the knowledge of the whole universe.

Erreur Trigonométrique
This figure show that all this above function are quadratic ones. The sine or cosine curve are denoted there by (1) and the red curve denoted by (2) is the Trigonometric wellknown [{sin(wt)=y].
We can see that there are errors from this latter compared with the Dakhiometry ones that are parabolic functions.

Note that this above formulas are only simple transcriptions of the Dakhiometry's spatial structure towards simplistic Algebra numerical formalisms.
But in their spatial structures it can be read directly the sine or cosine of an angle and also they figure out directly the given angle. That is to tell, in a spatial structure an angle is not directly read only as its sine but also as its inverse denoted by the Arc-sine.

- equivalence point from second derivative curve (, Singapore)

- describing sine and cosine (, University of Minnesota, USA)

- animasi trigonometri matematika (Indonesia)

- graph sine 0-90 degrees (

Example of the coagulated Mathematics

What can Mathematics know about a parabola? this latter is there diescribed as defined by a director axe and a focus. From there complicated algebraic functions tempt to defined a such parabole.

Here in the following we will see what is a parabola according to the Dakhiometry.

- ordonnées à l'origine parabole (Canada)

- parabolas in real life (, Telephone & Data Systems)

- parabolas in everyday life (, Texas Education Network, USA)


- Mathematical parabolas (Germany)

- parabola equation math (, Romania)

- general parabolic equation (, Imperial College, London, UK)
- mathes formule Iran

- accurator parabola (Indonesai)

- Iran maths (Brunei Darussalam)

- parabol arc quadratic equation (, Vietnam/Australia)

- mathematical definition of parabola (, Okinawa, Japan,

- maths tool Singapore (Singapore, _iszZx0ntq_Q/SokofUWCezI/)

- parabola feed (Korea, parabolic/parabolic_reflector.gif)

- parabola ends of lateral (Philippines)

- Foyer parabole (, Tokyo, Japan, 0258/forum_258808_2.png)

- parabolas in real life (Cocos (Keeling) Islands, Costa Rica)

- Rational + pole + Communication + png (Korea)

- unique + real + life + parabolas (

La parabole n'est pas ce que les Maths dit

An unique particular parabola and more generally, a given parabolic trajectory, can be defines precisely with unbounded space parameters.
This figure shows that a given parabola (P) can be determined by a focus (F) as the center of the series of cocentric circles and any isoscele triangle. One of this isocele triangle side pass through (F). Its other side should be parallel to one unique given direction. The parabola point is then defined by its vertex resulting from the intersection of thes two sides. This figure describes how these isoscele triangles are positionned when the fixe direction of one of the isoscele triangle is parallel to it symmetric axis.

a) - A parabola is not generally defined by a focus and an axe director.
b) - A parabola should be defined by concentric circles as Focus and by a fixed direction.

- for + every + angle + there + is + axactly + one + angle + bisector + true + or + false (, USA)

It is true.
Absolutely, we have to take any angle as the unit one. Then we have to anlyze this problem as follows:
In the Natural Interger series, what can be divided by TWO?
Therfore, from an unit angle, only EVEN quantity can have a bisector. It is only a true concept over the universe Fact.
This the rational logic applyed to the dicrete matter: only even quantity of elemental matter can be exactly divided by two.

However, in our condensed matter world, we can't never have the elemental matter exactness. It is why in the particular exactness of the condensed matter approach, we can tell that ANY ANGLE has NECESSARRILY AN UNIQUE BISSECTOR.

Dakhiometry as a true new science

Matter Space has two fundamental characteristics:
1) - Angular or Directional type
2) - Linear type
3) - The two characteristics are unified according to a Space Constant for mutual Transformation.

The old Mathematical Geometry are not space science but is only empirical approach to some incomplete superficial formalism.
While the universe fundamental basic first reality denoted as space is fully mastered by the Dakhiometry science. Space is quite known and practised through its linear and curvilinear aspect.
Practising space is a clear conscience on Measurement. It is based on:
a) - A just conscience on Quantity and how to determine it.
b) - Measurements are concerned on the two space aspects. It is how to determine: Linear and Curvilinear Quantities.

Knowledge on Space is a quite fullness of Dakhiometry conscience. That means: the Dakhiometry practise a true basic Science Language that is composed of basic space elements.
The current official Mathematics have no means to get a little sight in the Dakhiometry science because the current official science all along the Time and through all different epochs, ignores what is Space.

Accuracy of angle according to the Dakhiometry method
Property of space point is to be successive. It concerns for the Linear realm and also for the Curvilinear one.
In Dakhiometry a precise mode of Angle determination is to correspond point-to-point from Linear to Curvilinear.
This means that the ratio determined in the Straight line can be applied to the Curved line. Therefore,
as we can do on linear realm all the four calculation operations, we can applied the same possibilities of calculations in Angular realm to masrer constructions of any spacial figures.
Thus, linear calculations operate on distances and curvilinear ones operate on angles in space. The precision is the one of lines intersections. Note
* On a straight line, points determine distances.
* While on a circle, points is directions -or angle- determination.

Here is an example of Mathematics ignorance.
Everybody believes that he know what is an ANGLE.
*   Mathematics ingnore the three basic modes of space determinations: the squaring a circle, the trisection of an angle and the doubling a cube. This is a proof of a quite space Ignorance.
*   Science ignorance is shown on how it ignore the Quantity and what is the Counting. Numbers are only a Holly Trick for chatting that give to men the illusion of telling science.
*   Trigonometry is a same trick to overcome the Angle ignorance. According to that Mathematics don't know how to square a circle then Mathematics ignore what is true or false about Linear and Curvilinear data.
*   Consequently, was born the Analytic Geometry. It gives the illusion that science is mastering the measuremnt of the World and wield power the Nature.
A simple example on analitycal geometry: with a so called y=ax2, Mathematics prove that a parabola is an Ignorance.
This seems an immoderate expression, doesn't it?
So, do you know that a parabola is a pure space form as a circle, a square, a triangle,...etc, are a pure space forms? Here is what is a diagram of successive conic space structure:

Space conic structure

- real life parabolas trajectory (, Oklahoma, USA)

In consequences, do know how to place anywhere in a given space structure, a parabola or only one part of it? Mathematics have no means to do it else than with illusive manipulations. Because knowing what is a space conic else than its analytic forms, you can tell that you know what is space!

Ignorance of Mathematics gives rise to ignorance of all the different Physics Théories where everything are weird harmful tales for human.

In conclusion
In addition to the Linear World, the Dakhiometry masterises also the Science of Angle in the true universe Space.

The mathematics infinitesimal belief

Discussions :

Conditions of space transformations is necessary a reversible process.
In this case, these transformation should be done according to the following properties.

Line to curve Transformations A line (x) represented by infinitsimal unit (dx) seems to be confused with any curvature (C). If this statement is true there should be a property continuation linking line (x) to the curve (C). There is thus a relationship represented by the way (1).
In this case, a such relationship may be valid in the reverse way (2).

However, aside some particular cases of function,
there are many results of such transformations given by the uses of integral and its reverse derivative calculus. These results are :

1) - An integral of a linear function versus a linear variable, gives ALSO a linear one. There is no continuation along the way (1).
2) - An integration of a curve give ALSO a curve. There is no continuation along the way (2).

3) - A derivative of a curve is ALSO a curve. There is no continuation along the way (2).
4) - A drivative of a straight line is a constant. There is no continuation along the way (1).

Result of the Dakhiometry analysis


An infinitesimal of a straight line is always a straight line.
An infinitesimal of a curve is always a curve.

One may remember that the squaring a circle is a reversible transformation. Therefore, in space, curve and straight line can be linked.

Finally here is a remark about the Infinitesimal object property when it is used as integral and derivative calculus. Generaly, for these purposes a curve function is used with a linear variables e.g. as (dx) or d(t). Then,

- The integral and derivative functions cannot give exect exact results according to that a linear variable cannot describe exactly a curvilinear function.
- The property of a curve and the one of a straight line, do not depend on the scale that one consider them.
- Curve and straight line are different spatial structures.
- More precisely tell, a linear VARIATION variable does not correspond, one to one, with the curve ones. Even if there is a one-to-one point, it can't be possible to get the complete correspondance between linearity and curvature.

- "exect" + measurement + for + pie + 3.14 (Brunei Darussalam)

These conditions concern all the infinitesimal calculus, include the developments of functions. Using these methodes are rough approximations when applied on curves. Ideas of using tools as infinitesimal means to reach any spatial structures are quite false. The above example of circle surface calculation proves it. Fundamentally, it is quite an error to believe that infinitesimal objects may allow to reach into any spatial structure.

The important usefullness of these results, is to show that really there is a belief concerning the INFINIRESIMAL mathematics methods. Believing that any infinitesimal displacement in a straight line is equivalent to a displacement on a curve is the false axiom in mathematics. Remind that infinitesimal is the basic tools for Algebra.

Finally, there is really a key that allow entering the circular form. the Squaring a circle is the ONE and also the UNIQUE ONE to open the circular structure for spatial knowledge. It is not exaggerated to tell that the Sqaring a circle is the key opening to the universe space knowledge.

- unit + circle + for + "calulus" (Canada)


It is possible to obtain the circle "area" value in doing measurements and also with the integral calculus. Note that all the integral calculus calulus and its derivatives are empirical methods.
This two empirical ways don't need to know the Pi value. The squaring a circle was regognized as impossible then, it is straight forward to invent the Pi value as the circle "area" divided by its radius squared. One can verify this invention in doing a such measurement or using integral calculus. From that, it is find the Pi value exactly the standard one used in the whole world.

The most interesting result is that this 3.1416 EMPIRICAL VALUE, is raised to a Trancendental an Irrationnal number !

Empirical means are useful. However, one can't paste on empirical method a Transcendental and Irrational concepts. It is a contradiction of incertainty concepts that transforms thing into miracle.

Now, this Pi value obtained by empirical method, is the result of many square roots and Euclidean division calculations, according to Algebraic methods and principles.

On can conclude that the above error value of 1.34% on the surface calculations or measurements, are a general characteristic of the imprecise Algebra method.

- He + defined + the + value + of + pi + 3.14 + used + to + find + the + perimeter + and + "area" + of + circles (USA)

Quite exact ! He put the cart before the horse !!!

- archimedean + axiom + wrong (Croatia)

- pi + used + in + inertia (USA)

Actually, Pi should be an inertia symbol of wasting one's time on never touched goal as the Achilles' Tortoise.

- what + number + did + the + pythagoras + fear + since + it + lies + between + the + only + two + integers + that + can + be + both + the + perimeter + and + "area" + of + the + same + rectangle (Canada)

It was anciant and is presently metaphysical human psychology. The most important problem is not to find what a number is or is not. It is to take conscience of difference between spatial structure of the universe and human language. In anciant time and also today, space did not exist but there is only nothingness. Relativity fields are not space. They are objects replacing the ancient ether. Knowledge of space was masked by the natural capacity of human to produce his language. Thus, lookning in nature, it is natural to observe that things can be counted. But between things, there is always something. A such "something" is inexpressible by words of langages. As nature is filled by gods, it is obvious to attribute this inexpressible things by irrational concept in language. However language is not Mathematics. Therefore, in the futur, mathematicians have to invent how to build a language capable to "discribe" describe the space with High Fidelity. At this time human and also mathematicians wil have no more reason to be fear by these mysterious "converge but never touched" beings.

Is Pi an irrational number ?


... if negatve result with Robotsearch then, somwhere is nowher...

In the absolute space no irrationnality value is allowed. This is due to the foundation principle of discrete matter laws.

Now, because it is presented here a Pi formula where on can see there full of the square root of two symbol, then thinking automatism of mathematicians bow to the irrationality of the new boen number of Pi.
No, Pi is not transcendent nor irrational number. So, because a so much persons automatically to the look of formalism, I show here an another formalism for Pi formula and I am waiting for reaction to this new formula formalism.

- What + is + use + to + describe + the + motion + of + a + body + "aroud" + its + axis (USA)

- impossibility + squaring + the + circle + proof + of (, Välkommen till Uppsala Universitet, Uppsala, Sweden)

- full + pi + length (USA)

- why + is + impossible + for + squaring + a + circle ?(USA)

- squaring + the + circle (Belarus)

- mental gymnastic circle rectangle (Portugal)

Actually. A not so obvious one... - which one is height and which one is length in rectangle (Canada)

A real anxious problem. Why a North is the North and a South is the South, a 1 is 5V or an On and a 0 is a oV or an Off?

- a circle and its tangent which show the properties at the point of tangency. (Carolina, USA)

- squaring + the + circle + to + high + accuracy (, USA)

- transformation + of + a + circle + into + a + square (, University of Alabama, Tuscaloosa, Alabama, USA)

- in a square diagram what is length and breath% (United Arab Emirates)

Here from (A) to C1, it means a length of space structure attached to square root of two.

Pi length - " SHOUT NEVER" (, Bibliothèque National de France, France)

Resume to this figure:
Let SAD the greater square surface of side [AD] et SAB the one of the little square of side [AB]. The ratio of these surfaces can be written as :
SAB/SAD = Pi/4

Calculation of Pi lenght is done around the initial circle of diameter AD. Then le lenght Pi is as follow.

If the little square is the transform of the circle [C]. Then the Pi value is directly given as follows:

Pi = 4..(AB2/AD2)

or :

Pi = 4.(x2/y2)

Also, we can write :

Pi = 4/(AD2/AB2)

You can use these two formula for Pi calculaation concerning any dimension of figures. ANY DIMENSION is valid to obtain the Pi value given in the following formula full of square roots of 2. This means that any number in the whole universe is "irrationnal". That is really a miracle !!!

In brief:
These equation are quite rational. And they prove that the following formalisme is also RATIONAL. And consequently, Square Root of Two is necessary rational :

Pi Détermination

This last formula was determined to prove also that the numeral Pi is a universal constant INDEPENDENTLY of the surface formes. It is only a surplus of proof because considering the surface ratio as ratio formed by squared numerals then, the constancy of Pi is enough explicit.

- boo + boo + boo + square + root + of + 2

Therefore, out of any ideology, who can find some reason of the irrationallity in such a formula ? Because the numeral Pi cannot be at the same time, both itself and its contrary.


- "ration" + between + diameter + and + circumference + of + a + circle (USA)

In the opposite case, everything is irrationnal, even the integer natural number series. So, according to this formula, the Pi value can not be an irrational one. Because [4] is a rational number and the ration ratio can be written with any possible value. In consequence, if Pi is irrationnal, all existing numbers are also irrationnal.
The above formula proves that
the statement of "Pi is irrational" is an unescapable contradictory one.
Conclusion :
Therefore, Pi is necessary a rational numeral.

Now, there are many who complain or enjoy that the numeral Pi seems not finish to calculate. But don't enjoy with it, I am sory to remind them that they don't know how to divide. And also, they ignore that they fon't know it. To enjoy more note that most of numerals division can't never finish to an exact value.

Remind that the division use the Euclide's division algorithm. This process is generally not an exact dividion. Mathematics don't know another method to divide. The reason is of great funfamental one and even for a mathematician of genius, Pythagoras is a magnificient example, we must know that : numeral is not mathematic but only obey to human language rules !

- what's + the + square + root + of + one + third + pi ?

- how + can + you + proove + that + the + square + root + of + 2 + is + irrational (Canada)

- What + is + the + reason + to + find + the + end + of + pi

This is the main question.

Predict + pi + nth + decimal + place ?

- "FORMILA" + DE + PI (Mexico)

- "area" + of + a + circle + "formila"

- numeral + handwriting ++- kid +- kids

- how + is + pi + determined + so + exactly

The problem is now to replace the whole calculation system with a rational one that allows to define the exactness of space. This needs more than some remedy recipes.

Does squaring the circle done when the perimeter or the surfaces are equal between them ?

What must be said clearly about the squaring a circle.

The squaring a circle can not be done in the equality of the perimeter between the circle and the square !

The squaring a circle can not be done according to their perimeter equality.

The squaring a circle is done under the following unique condition:

Both, the perimeter AND the surface of the circle

are equal

to only the square surface.

Transformation of a square to a circle can be done initially with the Surface OR the perimeter of the square, to find the Surface of the transformed circle. Reason of these conditions rests on the unique correspondence between a numeral and its square and inversely. Example : let [x] the length of the square Side OR the circle Diameter. Then :

4.x = x2
and thus :
4 = x

This result is unique and immutable. And the squaring a circle with its reciprocal, are done always with this factor [4] that is a part of the constant denoted Pi.

It is why in the Dakhiometry, it is only considered the figure of a circle Quarter inscribed in a Quarter of Square.

To remember it :
TWO values of the one corresponding to ONLY ONR SURFACE of the other.

- "perimetr" (Gorgia)

- structure + of + matter + "expalined" (Canada)

- Why + is + there + also + + Pi + in + the + "perimetr" + formula ?

This is a main point to understand why there is Pi. From that Pi appears as a space constant and not as a particular effect of a circular form.

Pi is only a proportional factor that appears in a homothetic space transformation. This is explained as herefafter :

A figure "area" is the result of two lenghts product
and can be write as
kx.y                    (00f)

Then, any form of plane figure can has their "area" written as under the above relationship (00f).
For the square :
with k=1; kx = y;    it give: y.y = y2
For a rectangular surface :
For circle surface:

And a circle known form is :
ky.(y) = Pi.y.(y) = Pi.y2
in that k is denotted as follow : k.y = Pi.y
Therefore Pi appears really as a length homothetic factor.

For their perimeters
Square perimeter = 4.(y)
Rectangular perimeter = k.4.(y)
Circular perimeter = k.4.(y)
and in a more usual form :
k.4 is denotted as follow : k.4 = Pi.2
Pi is also a homothetic length factor particularly applied to circle because circle and square are invariable closely related forms.

In a product of lengths to describe different forms, it can be use a same length for all this forms and the remainder can be seen as a different homothetic lengths. According to that for tha the square, rectangular and circular forms, it can be seen that they have a same length (x). Their differences are then "discribed" described by other homothetic ones as described above.

Pi is only a homothetic constant used for circular figure, generating from a square form.

This is due to its Geometric origin. Because Pythagoras had begun to know the square. He applied it as the basis of his Geometric developments and also for his number theory. But the fact that any form are derived from the square is only a very particular case known by Pythagoras. From this epoch the World is formed with some given particular forms that are only hypothesis built from a limited knowledge on the universe.

In conclusion :
Pi is usually known as attached to circular figure but Pi is not a property of circles. Now, we have to understand Pi as only a constant factor use for homothetic space transformation.

- Indian + mathematician + created + a + formula + to + rapidly + calculate + the + value + of + pi (from .us)

How + to + figure + Pi

The Pi value as a straight length

From a circle {C} inscribed in a square of side length AD, one can obtain a litle circle {C1} charactérizing this spatial system. Placing {C1} at the center {O}, a segment [AB} tangent to it can determine the side {AB} of a square. This latter is the squaring of the circle {C} and has a surface equal to the circle one. The Lam-Ca theorem shows that the surface of the rectangle colored in cyan is also equate to the cercle {C} surface. In consequence, in this rectangle if the side {AD=4} then the other side {AB' = Pi}.

Results :
1) - The cyan rectangular surface is equal to {4 . Pi}.
2) - Examining the formula {4 . Pi}, one can see that it represents also both the surface and the perimeter P of the circle {C}, when its radius is R = 2. According that :

P = {2.R.Pi} = {2.2.Pi} = {Pi.22}


From a length of 4.Pi, one can obtain any rectangle having this surface value. Using the Lam-Ca theorem one gets a square representing this rectangular surface. Then, the reciprocal of the squaring a circle can give the circle {C}. This circle {C} has necessary the perimeter {4.Pi}.

Any circle can figure out the space Constant
of a squaring

- Do + we + know + today + the + exact + value + of + pi (Canada)

The old pi values are empirical or mystical given value. This last is a given quantity to aplay blindly. There is no means to know why and how they come from some origins. While the new pi value 3.12 is an exact value. The exactness of it is founded on the spatial structure from there it was calculate. It is spatial reasons that come from a direct proof reciprocal one. Exactness that come from its universal presence in any spatial structure transformation. This value that can be figure out from spatial figures and not from arbitrary discouse rules. This new spatial Constant is fully exact and universal. It remains now to found how to precisely numerise it for usual human language.

- new + geometric + construction + pi (Philippines)

- pi + is + rational (Lithuania)

You are quite right, immutable right. Because there is more deeper reasons that there is no irrational things in space. More latter I will expose the complete means of how to calculate with spatial tools. In space a solution is a precise point in the fullness of a structure that composes the absolute discrete universe space. This allows the real accurate and precise life construction. There is no need to converge something toward somme unknown thing as one do it in the anciant times.

- pi + recurrent + formula (Russian Federation)

Remind that a quarter of circle is inscribed in a quarter of square. We will used this characteristic to obtain this space constant for any circle during squaring transformation. In fig-4-4, with the circle diameter AD = 4, figuring out the length Pi is directly the AB' length. What can we do when the diameter AD is different; AD from 4 ?

When AD is different from 4, in this figure, AB' is also the length Pi. But you must normalize this length on the diameter AD as follows.

Therefore, in a general figure dimension, we have the Pi length as :

Pi length = (AB').(4/AD) = 3.12019373...

- "cricle" + perimeter + equation (UK)

- Find + a + function + that + models + the + "area" + A + of + a + cirle + in + terms + of + its + circumference + C (USA)

Actually, there is the Constant relationship between the circumference (C) and the "area" (A) of a circle. And precisely it is due to the Space Constant as shown above. Then, if AD is its diameter :

(C/A)circle = (4/AD)

Or explicitly considering the above figure,
In any circle the Constant length of Pi is given by a constructed line AB' as:

Pi length = (AB').(C/A)circle = 3.12019373...

The square has the same property in relationship. Then if AD is the square side we have:
(C/A)circle = (C/A)square
Ce qui veut dire que la longueur donnant la Constante Pi est aussi:
Pi length = (AB').(C/A)square = 3.12019373...

It is the only unique simple constant relationship between perimeter and "area" of a figure. The same relation is seen for a circle cricle and a square shown that the square inherits the circle property according to the squaring operation. It prooves that the circle is the UNIQUE and PERMANENT matter space structure and that the square is directely the result of this transformation.

Note :

The universality of a such spatial constant is a fact of the immutable UBIQUITY or SIMULTANEITY property of the space matter.

- absolute + value + proof + for + any + number (Canada)

Any number can thus be transformed into natural number. Il suffice to change the Reference length value of a construction. It is the case of a "unit square". Therefore, the Division Algorithm is only a practical method for approximative calculations.

--- Change to Unit System ---
The Space Constant (3.12019...) used as
...........UNIT OF SCALE

Any figure system can be nomalized on the Space Constant.

For this purpose, it suffices to determine in this system a length (Dint-ref) as the internal reference length.

From (Dint-ref), will be normalized this system with the Space Constant to get the unit of measurement.

It suffice to multiply any measurement in this system by the ratio (4/Dint-ref)


This is the proceed for a generalisation of norme for space measurements

If there anywhere in space other alive planets, it should exist necessarry a such space normalization for a unit of length. It is the one necessarry normalization process because the Space Constant is a remanence of the Permanence. There is no other Permanent form like the circle one which is the universe one.
It is why
Getting the possibility of a such logical Unit Normalization, we are yet possibly entering and standing in the UNIVERSAL SPACE!

Practical exemple
Suppose that you are trying and verifying the Square a circle construction. You like to have from a remote friend some opinion about it. This latter will do it and on his computer, realizes this geometric construction according to his usual manner. That is probably with a figure quite different in its dimensions than your's one. Thus, he can rapidly verify the different relationships between the geometric elements. Finally to give a brief result, he can do a numerical measure on his computer and then tels you his solution. His numerical result will be understood by you because he is applying the normalized space Constant as you do it yourself.

There is no problem if your remote friend is an extraterrestrial one that is living in some remote stars...

- VALUE + OF + PI + ACCORDING + TO + WALL + IS (India)

- proportionality + L1 + L2 + S1 + S2

Value of Pi is also given as :

Constant = 4(S1/S2) = Pi

S1 and S2 are surface of circles or squares denoted in figures of this text as the C1 and C2 diameters.

On this day, october 2006, since november 2002...
My first point of note is the following.

The sad fact...

The squaring a circle was revealed since four years, on this Earth. By the Squaribg a circle, the New World is thus created and displaying. Particularly, in full view of all mathematicians.

And what is the result of a such event? Because this is a Unique events: the real world is creating, the reality, The One.

a) - Nothing is never notice by official institution, nobody is refering to my works. It would be a sacrilege to open an institutional mouth and tell: the squaring a circle is a fact of human life, the human evolution...

b) - What are most of you worrying? Its is something like "Archimedes' Pi", the longest Pi, the irrational Pi. Thus most of people is still living in the deep darkness of the Pass. They are dreaming all along their life and can't see what is the Here and Now.

c) - Probably, most are telling that the squaring is not so important. May be, this true proof doesn't be a true because it isn't the work of their own Official National Idolized Great Genius.

Duration of four years to make acquaintance on the so simple squaring a circle proof... and no official Scientific Institution Intitution is abble to understand its importance impotance! This a miracoulus constant of the human darkness capacity, the Fantastic one.

- "Impotance" + of + zero + in + mathematics (Mauritius)

Exactly. Zero is impotence as a number because it is not a number. Its invention usefullness is to give to human language to express the cyclic succession. Zero is is not reality. And in the universe there is the most basic logic that is the unity. Because one matter property is the succession of recurrence. A recurrence is only possible if it starts from unity. With this latter, a recurrence can unfold endless. The unity is not the language symbol (1). Unity is a logic concept. Any object can represent Unity. I will show it with linear and circular spatial figures why we can use the language terms as 1, 2, 3,... that are not mathematic figures.

- Hand + and + Arm + Gestures: + "The + OK" + sign + is + interpreted + in + Japan + as + the + symbol + for + money,+ because + the + circular + shape + of + the + index + finger + and + thumb + together + suggest + the + shape + of + a + coin. + In + Argentina, + Belgium, + France, + Portugal, + Italy, + Greece, + and + Zimbabwe, + the + sign + means + "zero" + or + "nothing". + In + some + Eastern + European + countries + as + other + countries + throughout + the + world, + the + gesture + indicates + a + bodily + orifice + and + is + highly + offensive (, Romania)

These gestures are used here as "word" signs for language expressions.
The "OK" seems to me as telling that something is Okey or "Fine". Fine as the thickness of a hair between the thumb and the index.
However, may be, the Zero as India mathematic symbol (0) is refered as a circle, representing cyclic process figure. It is the case for any numeric base, that allows cyclic counting notations for great numbers.
So your informations on hand and arm gesture languages are very interesting for good relationships between human mutual understanding.

- "impotance" of the centre of gravity (UK)

The importance of center of gravity definition, is the first basic datum need during interaction. However, when center of gravity is a real measurement impotence, it gives rise some difficult problems.

- "intitution" + mécanique + en + France (Canada)

Why the Squaring a circle is a Creation of the New World? A new world is a one that should replace the old false world. Thus here are what the False and what the New are.

What are False?
1) - The false is the erroneous concepts of Number as ontological facts in the universe. Number is only the human notions invented by Human genius while ignoring what is the Space where they are living. Therfore, necessarily numbers inherit the human irrationnality property.
2) - Ignoring Space, the earlier human genius ignore what is the difference between circularity and the straight line. Consequently, They ignore what are Distance and Direction.
3) - With all these basic ignorances, the old human generations ignore what they denote as their sciences. This latter are only empirical and ideologic dogma that belong only to belief types.

What are true?
Only matter space is the basic ontological reality fact. Only space is the fundamental essence and materials of the universe construction. Only the space is the true language of the action for life. Only space is the basic structure of human thought logic.
Therefore, human should name eveything because he thinks. The basic names of the reality are the concepts generating by reality facts. These basic names do not be the human language speaking or writing words. True concepts are reasons of thought and not words of the talks.

Numbers are only words. They can't be materials for knowledge. Thus the thinking needs authentic concepts badly denoted as numbers. Then, the thought needs to name the quantity in physic reality. These names of object realities are not word but space construction. Therefore, naming a space length or distance, is actually the how to construct precisely this quantity. What is the real concept usually denoted as a number, is in fact how the human thought can situated precisely this object quantity, in constructing it. Thus a length or a direction being able to be named in our thought, is in fact the know how to construct according to space language. This are in daily practice needed for each of us, the know how to move in gestures or in displacing.

In summary
1) - The false of the current sciences.
Human genius are buried in huge errors as they are living according to empirical manipulations. Sciences do not know what is a Length and quite ignore what is a Direction. Thus, they do not know how to precisely name a quantity, the actuel space quantity. More deeply, he cant have some precise things about circular space structure. The Trigonometry is an approxiamte trick as well as the Archimedes' polygonal convergence for measuring the circle. None of the mathematicians can have a just idea of the Angle Trisection and the millenary unresolved three basic mathematic problems on space.
The Trigonometry is an approxiamte trick for calculation as for the whole Algebraic methods. Because the ANGLE quantity is a quite erroneous concept of the Direction in space. You don't trust on my remark? So, I ask you to only draw any precise angle. Only draw, any angle given between the whole azimut direction. And also, draw any given length of a segment. Please, if you dont succeed to do that with the compass and straigth edge, then you have to conclude about of the great ignorance of the official sciences and with what you are educated during generations!

2) - What about the New World introduced by the squaring a circle? The squaring a circle is the basic knowledge starting at the universe construction begining. Thus:
a)- ANY SPACE LENGTH CAN BE NAMED. That is to say, any space length can be constructed. Quite precisely and fundamentally in the elemental discretness precision.
b)- With the squaring a circle established. The Direction is also Quite precisely determinated in space, as it does for the straigth length. Thus the space Direction is not defined as in Trigonometry by the Angle. Therefore, with the reality of the squaring a circle, ANY DIRECTION IN SPACE CAN BE NAMED.

Would you draw precisely a given "angle", divided an another one, would you like to inscribe (n) gones given in a circle? You can do it now, EASILY. Easily,.. however, remind that its a millenary enigma for all the human existing mathematician genius!

This two basic human mind conquests, is resumed in the event of the publication on november 2002 of MY OWN SQUARING THE circle WORK. The quite disdained by most of the whole so Official Today Mathematician Genius.

So, the latter conclusion is for me: the real 3th millenary event of the official human ignorance, the huge Big One. I take off my hat to them, the big champions.

Now, I challenge them to determine themselves what are these squaring-a-circle consequences that I am telling above. In the opposite case, it is faulty to remain in his errors when the true is present.

Note that any value {q.Pi} is also valid. Therefore, any fraction of Pi is a measure of a straight segment and a perimeter of circle, provide that any number is a square surface and any other derived forms as a rectangle of the figure-4-4. We can state it as follows :

Theorem of the equivalence
between a circle perimeter and a right segment :

Any circle perimeter can be precisely straightened and inversely, any straight segment is an exact circular perimeter.

The rational circle perimeter

After construction of the length equate to Pi, as done above in figure-4-4, we can see in this figure-4-5, the construction of any perimeter of the universe circles. Each perimeter is equal to the surface of a corresponding rectangle.

On this figure, any perimeter of circle Ci is equal to the corresponding {xi.Pi}, that are the product of the rectangle sides, {xi} and {Pi}. This construction is valid starting from the quantum matter to the maximal value of the matter in the universe. All these rectangles haves a constant side equal to Pi.

The figure-4-5 shows the rectangular surface, with the length Pi as a side, measures the circle perimeter. Inversely, a circle perimeter, is the measure of a rectangular surface. There is an exact one-to-one correspondence between these two figures.

Conclusion on the circle perimeter :
1) - The constant length Pi is rational.
2) - Any rectangular form can be constructed from a circle perimeter.
3) - This agrees to the Dakhiometry Third Postulate on matter that states any object number can be considered as a square surface.

Therefore, from the starting of Evolution, it is why a thread can be coiled and uncoiled from a spool and a wheel can run on a road. One may say that it is obvious. But I think that any woman and man mathematicians necessarily have a secret question about this "length concordance" since the time where a circle perimeter was famous to be incommensurable with a straight line...

In summary:
The Lam-Ca theorem alows to define in the circle-square spatial structure a quantity that can be in four forms : the surface of the circle {C}, the surface of a square of side length {AB}, the surface of the cyan rectangle and also the Perimeter of the circle {C}.

Any perimeter length can be rationally contructed!

- algebra abstracts figures (Puerto Rico)

- geometry continuity (USA Wyoming u)

- rectangle and circle architecture (Australia)

- width Theorems and Postulates (USA)

- fantastic + facts + about + pi maths (United Arab Emirates)

- circle perimeter (USA Florida edu)

- Dessine moi un cercle dont la circonférence est un nombre rationnel (Belgium)

- "squere" root of (, South Africa)

- square roots sculptur (club-internet, France)

En effet, au compas et à la règle, comme les maçons et le tailleurs de pierre.

The problem is how to construct any circle perimeter equal to any given number particularly equal to any Natural Number.

It is esposed here a simple Dakhiometry method proving that any circle perimeter can be constructed. That is to say, any numeral can be spatially constructed. In consequence, there is no Irrational Number in the universe.

Here is the method, step by step reasonning, of how to construct any cicrcle circle perimeter.

Even if this construction is very simple, it prove that from millenarries the mathematical world is emprisoned in his dummy irrational ideology.

We will see here how a circle of perimeter equal to 3 can be rapidly constructed. The numeral 3 is know as a rational Natural Integer Number. It is an example that any number or more precisely tell, any space length is constructible.

1) - We begin to construct a square surface equal to 3.

From the basic universal theorem Lam-Ca we can do it as shown in this next figure.
Square root of 3 rational
Only the Lam-Ca theorem allow to rationally do this construction.

2) - Next, we need to construct the Space Constant in squaring a circle C, with the little circle C1. On this next figure, this construction is shown in blue lines. We get the Space Constant length usually denoted as Pi or Pie.

3) - With this referent Length as diameter we draw a circle Co.

- Representation of irrational number on a number line (India)

Any segment on a straight line can be a diameter for a circle. Then, any Number measuring this diameter can be represente a constructible number. More any square root of this diamater can be also constructed. This means that any irrational number can be constructed on this line "of Numbers". Therefore, there is no irrational Number, provide that all of them are constructible.
This is for particular constructions with the circle property. But there is in Dakhiometry, a specific spatial structure where constructions of CONTIGUOUS defined points proving thet there is no irrational hole between adjacent and successive segment lengths. This valid for any numeral base even for binary and hexadecimal ones. This shows that every numeric base are only conventional things for man-Numering-counting. The true Quantities are the one constructible an definable by spatial elements.

- wawe hot (Vietnam, 4431175665_470fb4f732_b.jpg)

- construct square root of on the number line (, The University of Texas at El Paso, USA)

- Only the Lam-Ca theorem allow to rationally - calculate by Iteration sqrt(3) (Israel)

- The Square Root of (, Hong Kong)

- geometrically construct root ( (University of Northern Iowa, Cedar Falls, Iowa, USA)

- "simplefying + squair" + root + example (Canada)

- NATIONAL SQUARE ROOT DAY (, NBS National Bankruptcy Services, USA)

- get real pi .. be rational (University of North Texas, Denton, USA)

- square construction methods gif (Algeria)

- Circle arc integration (Germany, Schaeffler Group LUK)

- does a circle equal a square (, USA)

- perfectly equalled sides (, Hungary)

circle perimeter

In the circle Co it can be placed the previous square of side equal to square root of 3.
Now with on the basis of the LamCa theorem, we can transform this square surface onto a rectangle of same surface, using the square of the side equal to the Space constant length.

We get finally the circle of perimeter equal to 3. It is the one the diameter of which is equal to one side of this rectangle.

Any circle can be rationnally constructed.
Therefore, the Space Constant is rational.

Remark Reasons of these construction rest deeply on the universe principles more than the ones named here. That is to say, this construction and its results are quite rational.

Any quantity of circle perimeter can be spatially constructed. More basically tell, there in no Irrational Number.

This present construction is only a one that show how there is no Irrational Number in the universe

The Dakhiometry can do such construction from any given quantity beginning from Zero to unlimited one. You may verify that Mathematicians can do a such complete resolution because there is no fundamental bases in Mathematics.

- inverse square root calc (USA)

- number + series + exist + in + value + of + pi (Pakistan)

- tangente 2 cercles - caracteristiques

- spatial structures (, Russian Federation,

- general characterstics of ethiopian rivers (Ethiopia)

Rivers of Ethiopia are all looking on to the inside of Africa continent. Because of the Ethiopia high reliefs particularly along the Eritrea ones that close any river to flow towards the Red Sea. So the Ethiopia characteristic is mainly to look on to Africa continent and less toward the Eastern.

Characteristic structure of a square

Here are the basic characteristic of the spatial structure of a square. This can be shown by the two circles C1 and C2. The surface of C2 is two times the C1 one.
The squaring of the circle [C] is thus precisely determined by these two characteristic circles [C1] and [C2]. Therefore the squaring of circle [C] is given by the side [AB] of the resulting square. And the precise length [AB']is the length of Pi value.

Actually, AB is tangent to two circles [C1] and [C2]. The reason is that the point {A], is the center of a hmothecy of factot h = (Square Root of 2) of the latter two circles.

The point [B] allows thus a precise and unequivocal intersection point in the square, for the squaring the circle [C].

Also, the angle [bAb'] = 27,96875154...° is the characteristic angle of the squaring a circle system. Il is talk about it in the following texte.

According to these square characteristics, the structure of a square allows the fundamental precise and accurate knowledge of the matter space. The knowledge property, or the physical interaction of matter, did not happen in the central symmetry motion. In this universe state, the EXISTENCE of the Perpendicular Fact was not set up.

- how + to + figure + circumference
- The length of PI
- delimited pi
- does a circle come from a polygon

- Religious + Science + belief + death (USA)

- anthropomorphism + in + Life + of + Pi

- Why + has + the + world + recognized + a + value + for + pi + for + longer + than + the + existence + of + irrational + numbers

How to figure out the square root of (2) and the square root of (Pi) lengths, with the compass and stratght edge

The length
of rational construction in the matter space

- "costructions" to the future (Italy)

- square + root + of + pi

- the + power + of + theorem + of + circle

- application + of + new + pi + formula

- square root of two (Canada, British Columbia, Burnaby, Inst. of Technology)

Note that square root of 2 shown here is not due to the diagonal of a square. It belong to a whole space structure of any ith-root quite precisely determined as construction. Because if a line is supposed to represent the current Reals Numbers series, in space construction, this same but real line can be described as a contineous nth-root in a continuation of discrete quantities. The example is shown above to define any angle cosisne by nth-root numerals.

- shows + that + square + root + of + 3 + minus + square + root + of + 5 + is + irrational + using + proof + by + contradiction (, Philippines)

- different kinds of spatial figures with pictures and meaning (Philippines)

- project k12 calculation of pi (Turkey)

- meaning + of + kkk + Philippines + flag + picture (Malaysia)

- Pecados + Mortales + Y + Veniales + Lista (

- north + Taiga + shield + animals (Canada)

Square root of 5-3

Here is the spatial calculation
of [sqr(5)-sqr(3)]. According to that irrationnal number definition is not constructible. This calculation is here quite constructible. I can't find any contradiction. There is irrationallity when algebraic method is used.
Therefore, there is a contradiction when one proves that this substraction of square roots is irrational.

- unicity + definition (, Cambodia)

- how do you answer A square with length 5 km (, Australia)

On this next figure, if the unit will be (1 km) then, length of 5 km is the diameter of circle (C5). Any other unit can be deduced from there according to homothetic forms.
Homothetic property is that it changes Distances in proportional forms but don't changes space Directions.
Homothetie is the direct property of the Central Symmetry postulate.

- circle theorems maths (Brunei Darussalam)

- square root (, Ireland)

- square root day (Biatorbágyi Kábeltévé Kft, Hungary)

- National Square Root Day (USA)

- geometric construction square root of two (USA, The University of IOWA)

- naturally occuring square roots (, California)


- square roots in ancient Indian mathematics (Australia)

- Cosmos square root of two ( (Purdue University, West Lafeyette, Indiana, USA)

In fact, any quantity from zero to the universe greatest one, can be writtenunder square-root form as successive discrete continuity. This shows that Numbers are strictly conventional formalism of words language. Numbers characteristics is that they don't obey and be expressed in true successive continuity.

write + a + program + to + approximate + the + value + of + PI + using + the + formila + given + including + terms + up + through + 1 , 99 (, California, USA)

- pi + are + real + geetrik (Greece)

Hereafter are figured out lengths of Square root of 2 and square root of Pi.
These lengths are rational provide that they are results of compas and straight edge constructions. These constructions are here given according to the circle Theorem, given latter in this text.

The square root length


The figure 4-4 is resume here to show how the square root of 2 and the square root of Pi are obtained. These legnth values belong to the number Q series.

The diameter of [C} is equal to 4 and the one of [C'} is its half that is equal to 2. You may mesure and verify that AE and AF are these values :

AE = Square Root of (2)
AF = Square Root of (Pi)

This is because :
AO = 2 x Square Root of (2)
That is : AB = 2 x Square Root of (Pi)

- hard math pie (, Minnesota, USA)

- really hard math equation with sqaure roots (, USA)

- Giant confusing math equation (, USA)

- longest math equation (USA)

As exposed here, this equation seems to be long. It is only because this method is a new one and have to be decomposed to be easily understood. But it is the most shortest way of calculation. Because how do we explain this following algebraic calculation formalism if we have to exposed it to an extraterrestrial being provide that he never knows what are our methods and tricks for calculation?

For example how do we explain this next formalism to kids biginners in math?
This next spatial calculation is done rapidly in the most short way if we are currently in use with the new spatial method of four basic operations as addition, substraction, multiplication and division. It is because the spatial language is an universal reality. It is not built according to so many particular human languages done with artificial conventions.
Thus, it is expected that in the futur, kids can rapidly learn, mastering and inventing spatial solution of most complicated technical construction problems. Until now it is not really the natural phenomena that are complicated. What is complicated is only the human empirical sciences that rest on their languages coagualted in formalism of algebraic numerical calculations due to their ignorance on fundamental facts of space.
Knowledge of space reality is in itself the action of humnan living.

- impossible math equation (USA)

In memory of Anciant math we can actually denoted it as the Impossible Equation.

- equation hard maths (Chile)

The difficulty of this present equation is not due to the spatial construction. It is because we are coagulated by the Ancient's math dogma. This latter is an empirical mode for decomposing things "world by world" as man use to "analyse" everything. Thus, old sciences are only analytical ways of understanding phenomena. You can note that any anciant proof of math theorem are done according to mathematicians' tricks of the trade. Rationally tell, these theorems are only verifications of remarkable figures.
A rational proof should be done from upsteam of any problem as for any river that comes necessarily from a source. For rational science, any construction should come from the perfect definition of the space. A construction is only possible if it rests on a space structure.
Therefore, understanding a structure means that our thinking should overcome the old empirical mode of problem analysis. Empirical analytic method can not but growing in complication of tricks and formalisms. Understanding a space structure should be a global or intuitive way of thinking.
Difficulties of resolving problems are due to sciences formatted by empirical mode of thinking. With such habit space structure seems to be Impossible thing. However, space structure is the real basic rational tool for human thinking capacity. Space properties are the most simple and wealthy natural language for human knowledge... only when old science dogma disappear from our habits.

- constructible numbers (, Coláiste na hOllscolle Corcaigh, Univversity College Cork, Ireland)

It is the rational number definition.
However Numbers are only language words to name the fact concept of quantity. Thus, numbers are reducing manner due to the discontinuity of language symbols to be abble to represent the continuity of the natural quantities. When Numbers are seen as the world physic archetype its discontinuity obviously seems to describe a world with full of irrationality holes in the universe.
In fact there is no hole in the universe physic. While there is really the science Number system full of holes according to millenary systematic errors. The Numbers are really inaccurate method for science. Obviously, human need language words but science should to reconsider that factors of reality is the quantity.
In Dakhiometry, it is seen that the universe space is characterized by the Distance and the Direction. Then, what is in space are necessarily characterized as a system formed in a quantity of locations. From there it is spatialy proved that the concept of quantity can be perfectly defined with the space properties. Thus, any quantity in the universe can be constructed in the continuity principle of the discrete space matter. This continuity of quantity is prooved with spatial element construction. Spatial construction resolution consists to resolve an unique spatial point as the intersection of two linear-curvilinear lines as a precise quantity of space locations. Therefore, there is basic rationally proof both for linear and curvilinear modes that there is no irrational hole in the discrete universe fulness.

- root size of Cleveland pear (, Canada)

How to get precisely your pear.

- actual + accurate + value + of + pie + .edu (Singapore)

- rational + new + pi + accurate + value (Netherlands)

- formule pi (Glaslokaal, Den Hagg, Netherlands)

- pythagorean ideology (, UK)

True accuracy of value OP shown on this next figure, is only the property of spatial language. But if one uses it as numeric digital then there are errors introduced by the bad Euclide's division algorithm and sources of error due to the Number Theory. All these systematic error rest on the Pythagorean ideology of Numbers.

- a picture of what Pierre de Fermat invented/the french number theroy (, USA)

- pi + accurateness (, Lausane, Switzerland)

- square root: Descartes' calculation (Serbia)

- EXPLANATION how was pi derived (Philippines)

Spatial calculations are straight from a given structure.
Thus, according to the Absolute space properties, a given structure defines by itself the relationships between points and lines. These relationships concern the quantities of points and segment of lines.
Therefore, what is for these quantities, a spatial structure explains by itself how to get a given quantity of a segment for example, that is related to its structure environment.
It is why the calcultations should be use the spatial method to deternime how from a given structure some quantity is related to it placement in space relatively to its particular structure where it is inscribed.
The squaring a circle, is then the only way to get the correct structure environment to determine the exact relationship between a circle and its another form non curvilinear as a square. This is the unique way to get the relationships between the Curvilinear and the Linear, these two basic aspects of the Absolute Space.
The Dakhiometry is composed with a complete method for spatial calculation in any complex manner needed. These calculations can resolve simply and precisely what is impossible for the usual Algebraic technique. The Numbers is only man's empirical means that give to the current science a millenary false idea about what is the quantities of the universe matter.
This next calculation for the Space-Constant (the old false empirical Pi) is a simple example.

The square root length

Length of Pi is calculated latter in this text as R4= (square root of Pi).
Then R4 intersecting with the tangent OM by OT is the square root of Pi.
This next figure shows also how to verify that
OT2 = 2.(OT') = OP = Pi

OT', with (T') as center of circle (O;T;P) with diameter (OP) equal to Pi.

- Square + Root + of + Pie + Formula (India)

Actually, this is a formula from spatial construction. It shows that square-root of Pi as well as the Pi are rational-constructible-values.

- how + can + a + rational + pi + change + the + world + of + computation (Canada)

To avoid error of algebraic formulas calculations, it can be choose to determine the figure lengths that can determine the new Pi value with only the usual relationship:
k2 = x2 + y2
where there are no need of the Euclidean division approximations.

- who + invented + the + accurate + measurement + of + pi (South Africa)

- what + present + impact + does + the + internet web + have + on + mathematics (, USA)

For example considering my personal case, I was during thirty years a laboratory assistant where I was only a simple dumb machine. Aside this situation, never any of my own work exposed in this web site was accepted by any scientific journal for publication. If there was no internet possibilities, the present squaring a circle remains still unknown and may be, for ever it remains as the glorious possibility of Mathematic Impossibility!
But still from year 2000, sciences are not yet intersted to replace the present precise Space Constant and was still prefering the old empirical erroneous Archimedes' Pi. In brief, this current world is really living a nigthmare and is not so optimistic.

- square root math jokes

- math equation solved with a miracle (, USA)

Actually, if overcoming difficulties in rational research on how to determine and calculate with spatial elements is a miracle... :-)
The results shown here are only the consequences from the knowing of how to do the four basic operations of spatial calculation. Any complicated algebraic formula can be done with such method but with rational precision and exactness in space structures. To get numerical result it suffice to use only the welknown rectangle relationship formula without suffering approximations of the Euclidean division for the number roots.
Squaring a circle is not a joke due to Hazard. It rests on a vast background of deep knowledge in space properties. The Impossibility Theorem for the squaring a circle is the example of how Mathematics ignore what is space. It proves that Geometry was stillborn mathematician vows and became rapidly formalism of human dogma.

- giant math equations (, Miami, USA)

Note that the four operations for calculation using spatial elements need at first to chooe any conventional unit of length that allows then to fefine length quantities according to this figure unit.
This is not an artificial convention but rest on the basic logic of successive quantitities of the ultimate elemental matter. In fact what is known as Induction principle for theory numbers is done on the base of the unit ONE (the 1 number). But mathematicians ignore that this ONE (the 1) is only a necessary logic representing the ultimate element of quantity. From there the Integer Number series can't never rest on the base of a ZERO. Zero is not a Quantity and therefore, should not be a Number.
According to this Number theory starting necessarily from the (1) the Arithmetics and the Algebraic need not to initialize a defined unit to go on calculation. Because Arithmetics and Algebraic are only in one particular case of Conventional Number beginning from the Number 1.
Spatial calculation of space structure needs at first to define a unit of length. It is because space has two main characteristics:
1) - Directions
2) - Distances.
In Direction one can access to the whole universe direction space. But in Distance the whole universe space should be define by homothetic considerations. This last space characteristic gives rise to the need of chosing measurement unit because homothetic realm is composed of different length scales.

- volume sqrt quarter substract (, Austria)



- C1 symbol (Philippines)

- grade 11 circle geometry (, Canada)

- struture + curve + of + in + Cambodia (Cambosia)

- concrete circles geometry (Puerto Rico)

Circle C1 - creative circles, geometry (Bahrain)

- geometry of solar cooker on coordinate axis (Ethiopia)

- geometry + theorum + and + pastulate (, New Jersey, USA)

- big tangent circle (, Germany)

Circle (C1) is really a basic little Big circle in the square-circle structure. Here is how to inscribe a square (Q) in the circle (C) using the (C1) as referent with point (P and P'). Also, how it determines a 8-gones.

Proof that the tangent AN to circle C1 intersect at point B to C2 and C

- Usa north carolina The Art Institute of Charlotte (, Moldavia)

- hyperbolic tangent circle (The University of North Carolina at Charlotte, USA)

- proof of a tangent meeting the radius at 90 degrees (, USA)

Here is this Proof:
Let any circle (C1) of center (O) and radius (ON) and a tangent (AN). Any tangent to this circle is defined as intersecting (C1) at one point (N).
Now let (N1) and (N2) the next preceding and the next susccessive points of (N) on the (C1) circonference.
Because the preceding and the successive point of the discrete mater, are equal in distance then:
(N1;N) = (N;N2)
They are two unit arcs of circle (C1). This means that the two formed angles are equal:
(N1;Ô;N) = (N;Ô;N2)
This is a reason to state that a tangent (AN) to a circle (C1), has the radius (AN) a symmetric axis.

Now, from Zero to 90 degrees, what is any existing angle formed by the radius (ON) and the line (AN) that can have the radius (ON) as symmetric axis, provide that they have only 1 common point at (N)?
1) - Zero is not an existing angle.
2) - While exclusively, two 90 degrees angles can symetrically disposed around the axis (AN) because a line (AN) is one direction with an angle of 180 degrees.

Tangent Theorem:
Any tangent to a circle intersect the coresponding unique circle radius always at 90 degrees

- TANGENT TIL CIRKEL (, Stofanet.Mine Sider, Denmark)

- crown radius and rolling radius (, Davis University of California, Davis, USA)

ON and OB characrerized by a square of side OB. - big circle and small circle with same tangent (Indonesia)

- when you trisect a triangle internally the intersection provides the vertices of a smaller traingle. what ever the original shape the smaller traingle will be equilateral. it shows the relationship of the random to the definite. (,India)

Really, there is no possible relationship between random and defined property. If a random is well defined, it is the negation of random. Inversely, defined can't never produce random result. They are two physiqcal properties taht can't never replaced each other. Physic are governed by the Uniqueness principle. That is to tell, for example, we never observe an object falling upward without the aid of a rational mechanism.

For the case of the trisector, it is quite governed by defined construction. If it seem to a process that produces defined from random it is due only to the fact that the Morley theorem was dicovered in inverse manner. The little defined equilateral triangle inside a greater triangle, seems to be the consequence of trisector constructions. It is only the result of the usual mathematics empirism method that proceeds only from consequence of a law to state this law and not from basic reason. In fact the Morley theorem should be start from the true source of trisector construction that should be done from any triangle property. Its final result should be the trisector construction and not the inverse that is the little equilateral triangle.
So, this Morley triangle should be really starting from the defined to reveal the defined equilateral triangle. There is no random. This latter is only the virtual world to designate what we ignore in the universe. For example, Mathematics has invented the Irrational Numbers because Mathematique ignore what is the Quantity uniqueness. Only language worlds is creating as Numbers to simulate the missing Quantity concept. This is the fact of irrational belief replacing the rational basic quantity.
When one know how to construct a triangle by constructing all its trisectors then one can construct any n-trisector of a triangle. Note that these constructions are additive operation and not dividing one. From there the internal little equilateral triangle appears only as a particular case of the trisector construction.
In conclusion
There is more much high interesting thing to learn than to repeat any of the empirical Mathematics trick product... Because without the space language, Mathematics can't do nothing else than to turn around a vicious closed loop.

- the + structure + of + mathematics (..)

According to the absolute space, any relationship is well structured. Therefore, when a problem is resolved then, its should be enligtened by a spatial structure.

Tangent to circle C1

Here is the proof that tangent AN to circle C1 occupies a specific position in the structure. It intersects at point B to the two circles C1 and C. Tangent AN is constructed with the circle C3.

It is shown above that aera of circle C2 is two times the C2 one. This the base of this proof. We will consider here the square of these two circle radius.

Therefore, in the triangle OBN is necessarry a rectangular one because the square of side OB is two times the square of side ON. And because the square of side BN is a right angle, the triangle ABD is also a rectangular one.

This is the proof that tangent AN intersects at point M the two circles C2 and C.

- biblical signs two circles (TimeWarner-telecom, USA)

- given two circles construct a mutual tangent to both (USA)

- history of unit (Vietnam)

The how to define the unit in space construction allows the mastering of spatial calculation, the perfectly precise and exact method for rational space manipulation. The Da-khi-Hoc is actually mastering a such method.

- David Brown base tangent comparator method (India)

Tangent to 2 circles

The solution is given when we see that all circles are homothetic forms. Thus, circles C1 and C2 are necessarrily homothetic forms.

This next figure gives the solution according to successive constructions numbered 1, 2 and 3. Beginning with the C1 and C2 homothetic center (M) determination with their two parallel radius (r1) and (r2). Then, the tangent (tg) of both circles is found with a rectangular determination with the magenta colored circle.

- the + length + of + a + rectangle + is + 5 + meters + more + than + twice + the + width + Express + the + lenght + "og" + the + rectangle + in + terms + of + the + width (USA)

Length versus width of this rectangle is given by the blue line on this next diagram.

Irrationality of a unit square diagonal is the expression of an incommensurate universe ignorance of Pythagoras and modern Mathematics

- unicerse (Mexico)

The unknown universe...

The circle is the reminiscence of the matter permanence from that the unicerse is endless constructed.

The above little circle C2 shows that the square root of 2 is inherent to the circle. That is to say, the square root of 2 is a Permanent universe quantity. Because matter is discrete, the square root of 2 is necessarily a precise quantity.

It is shown here the reason of how a square root of two is precisely determined, along a line formed by a successive localisation of the ultimate elemental matter.

- formula for diagonal of square (USA)

- Euclide to Pythagoras (India)

- Pythagoras secret society writing above door (, TDS)

- Secret Society 60th grade (, Sweden)

- physics measurement of length using set square (HongKong)

- common tangents of two circles (Indonesia,

Tangent to 2 circles
Rationnal square root of 2
The square structure allows to construct (C1) and (C2) in space to get square root of 2 length. Therefore, this latter is a rationnal and universal quantity. While a diagonal of a unit square is a dummy object because one cannot know what is a length=1. This latter is not a unique value.
A unit length must be defined as only a convention.

- art-square root of 2 (Point Loma Nazarene University, San Diego, California, USA)

- root lattice (Australia Sydney u edu)

Necessarry the discrete space basic latice structure.

- square root of 2 on a number line (Hongkong)

Resume the squaring a circle construction This figure is how to construct the circles (C1) and (C2). circle (C2) has its aera two time the (C1) one. They are includes in the circle-square structure. As all circles are homothetic figures, (C1) and (C2) are homothetic circles with the center located at point (o) of the square corner.
According their aeras the ratio of lengths is :

OO1/OO2 = sqr(2)

Therefore, along a universe line we can get any ratio of lengths equal to the square root of 2. On this next figure some of these ratios are shown as:


This is the proof that an universe line can be generated from the square root of 2. These lengths are exhaustively from the ultimate discrete matter to the universe length.

Now, Pythagoras and the modern Mathematics can tell that irrationallity is concerned only for the diagonal in a square of side equal to 1.

Precisely, this statement undelines their great ignorance about the universe Unity Principle.

What is the Unity Principle?

- what + is + the + unity + principle (, Vietnam)

The unity principle allows to define the universe quantities as a coherent system according to any choosen Unit quantity. For example the word Number 1 is not the absolute symbol representing an absolute length quantity. But it is any length defined as a concrete length quantity that can be denoted as the Unit length. For example, a given "table" can be choosen as the "table unit" for all the universe classes of tables. It is so for an apple fruit. A concrete fruit recognized as an apple is then recognized as a Unit fruit for all fruits of classes "apple".
Basically, it is from this principle that in Dakhiometry, any given length AB, can be used to represent all the universe quantities according to continous spatial constructions, exactly point to point. Any point on a segment AB can represent the space discretness of continous and successive quantities by spatially constructions. There is no irrationnal indetermined point on any length AB what ever its length is.

This principle means that the universe is composed by the Uniqueness Principle. According to that, any unique universe object is a Unit. You will understand it more easily with practical examples as following:

According to the Unity Principle we can take any Quantity as a unit of measurement. Thus, from any the following ratios we can choose a length for the unit of measurement. For example from:


We can state that Oa, Ob and Oc as the unit for measurement. Thus, we have:

(OA/unit Oa)=sqr(2)
(OB/unit Ob)=sqr(2)
(OC/unit Oc)=sqr(2)

Practical exemples of measurement systems:

Because OA, OB and OC can be any quantity from the elemental one to the whole universe matter quantity, we can see that the lengths OA, OB and OC can be as:

OA = sqr(2)
OB = sqr(2)
OC = sqr(2)

Because any quantity of matter length as OA or OB or OC, is precisely determined then, the square root of 2 is necessarily a rational quantity.

- who + discover + that + circumference + over + "que" + diameter + equals + pi (Colombia)

- is + pi + the + same + value + for + every + circle

For every circle, in a given spatial system of figure, a length Pi is equal to a same quantity, according to the unit choosen.

The modern Algebra BIG-BUG

How to do an error when one tells that in the square the diagonal is irrational with its sides

Convention of writing,

[sqr(-)] means [square root of (-)]

- simple + resume + for + "applay" + new + work (Autralia)

In a square form the diagonal [c] of side [a], the Pythagoras relationship is :

c2 = a2 + a2       (5-2-1).

In the continuation, by automatism of writing operations and not by reasonning, this equation is the transformed in Algebra as :

c2 = 2.a2       (5-2-2).

From this result, one established that the square root of 2 is irrational because the diagonal and a side are uncommensurable together. We see herafter that a such formalism is an great ERROR of reasonning

Note that a clumsy manner of manipulating this equation should be known only with the Dakhiometry Theorem General on Triangle.

The bad manner is situated in the deformation of the Pythagoras' relationship that is not a simple formalism that one can apply applay simplifivation and reduction. Then, equation (5-2-2) is an error that cancels the meaning of the Pythagoras' one. Example is seen in the destruction of the extended form of this latter. Here, the introduction of the term [2] is a fault of introducing an uncoherent datum. This fault is then undertood as the uncommensurable irrationality while it was only clumsy manipulation of numeral.

How to do not deform the Relationship of the Triangle ? It suffice now to understand the Dakhiometry Theorem General on the Triangle. Here, the equation (5-2-1), must only be written according to a coherent variables. One should not take an apple as a pear...

Then to seak the measurement of square diagonal [c], we can write :

c2/c = (a2 + a2)/c       (5-2-3).

Thus, the hypotenuse or the squared diagonal is :

c = (a2)/c + (a2)/c       (5-2-3).

Diagonal, square
Figure 4-5-3
From (5-2-3), the diagonal [c) is directly given by the Dakhiometry LAM-CA theorem as shown on this figure 4-5-3. That is :

a2 = c . (c/2)
et :
a2/c = (c/2)

Finally :

c = 2 . (c/2) = c

- Socrates + theaetetus + original + version (..)

According to Platoo Socrate had expalined to his servant how the diagonal of a square relatively to its sides is incommensurate and is an irrational root.

- square with diagonal (Massachusetts, USA)

The fact that one draws this circle diameter (c) and then, following the square (a2), proves that the circle diameter as square diagonal is directly commensurable with the square edge! This is due to the relationship structure property of the absolute space.
Therefore, the Pythagore's and Socrate's proof as reported by Plato's description and also to the modern Numbers Theory. all these irrationality demonstrations are false because the absolute space is ignored.

- 5 + pains + et + deux + poissons (, USA)

- Mathematique moderne classe de 2ième en France (Cambodia)

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- what + are + the + scienticfic + symbols (

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To define a number as a length

- math + words (

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- tales geometrija (, Serbia)

The Thales as like the Pytagore's theorem are only empirical relationship that rest on no reason then their practical verifying and recognizing practical applications. It is thus for most of Mathematics theorem that are nothing than from empirical method.
The true proportionality rest on more basic reason. This is used and rationally proved in the Dakhiometry that rest on the basic property of the ansolute Space. Even if one used to see and practise the Thales theorem, it is more fertile to know what are the reason of Proportionality. The Thales theorem is only the practical consequence of the space law that one should get in conscience to have a more reasonnable and fertile Science.

- myanmar students in massey university (, Nanyang Technological University, Singapore)

- horrible mathamatics (, British Columbia, Canada)

- mathematic history (, California, USA)

There is really a practical, simple and complete method of calculation of space dimensions with the usual four basic operations as addition, substraction, multiplication and division. It can perform as it is done in the current algebraic mode for any complexe calculation and for any root.

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- did + they + use + pi + to + figure + out + that + the + earth + was + round

OK. For everubody, the Earth should be ROUND !

- "eureuka"

About the irrationality of a diagonal relatively to the side of a square, proved by Socrates-Plato

- enlever + la + racine + carré + pour + trouver + l'inconnu + en + dessous (France)

- Game on the Unit Square (Bulgaria)

- diagram of the relationship between Socrates and Descartes (Indonesia,

According to the Homotheic property of linear space, a ratio of (diagnal/side) is always true because any circle from zero to unlimited side length is always rationally defined.

Let (d) a diagonale and (c) the side of any square. A little more complicate and because one know only the empirical Pythagoras theorem, it was used to establish the diagonal and side relationship as:
From there it was concluded that there is Irrational Number.
This result was only systematic error or only ideological consideration. Because the relationship {d ; c} is simply a rational ratio as:

(d/c) = Square root2(2)

The relationship between d and c is rationally found as follow :

- diagonal + of + a + square + is + commensurable (

It can be proved under many different constructions.

Diagonal and side

Diagonal and side Let (ni) any length of a square side and ABi its diagonal. According to Thales, we have:
ABi = ni.sqr(2)

In any square, a diagonal is directly and precisely proportional to its side and is spatialy constructible

In Dakhiometry construction of multiplication and division are known. It can be constructed

It can be find for any square the same length constant as:

ABi/ni = sqr(2) = Constante

"- what + is + the + laws + that + a + pi + can't + do ?"

...... :-)

- mathematic + concepts + - + square + of + a + square + root + theory (Canada)

Here is a a deep understanding of space that drive to fertile opening in mind.

One basic particularity of space that allows us to go through space knowledge, is what allows us to get the alphabet with what space construction way can follow.
Pecisely any elemantal fact of space is always a source. For example, knowledge beging on the formation of a square, like a dream that starts to transform itself in the reallity. Thus the elemental space, is alway the anterior of any construction of logic. The elemental space should be seen as the root of any measurement. It is why the basic space theorem is the Lamca theorem that state: any unit of space object appears in action with its squared quantity. There is not any fixe length or any fixed number. Thus there is no fixe unity. The unity is only the starting of a particular system because the most important law is the recurrence fact if matter. It why there are motion. From there energy as the square of motion, is the most important physic factor in the world construction. Because there is no fixed unity, the belief of a square or a circle unity are only human dogma. Most of us are educated to see the world as an eternal coagulated thing. Until modern Physics that considers the world as a geometrical fixe space standing in any time differential.
The matter consruction is always running forward. It is why in space, it is difficult to know everything backward. Thus, you can esealy make addition or multiplication of lengths, addition of angles but these proces reciprocal seem particularly impossible. It is thus the angle trisection that is the dividing of angle was never resolved until now. Because space is not conventional human language one can't lie to himself as it is practised in Numbers which is only conventional human languages. They are not universal truths. So everybody complains about irrationnality of numbers forgotten that it is not numbers that are wrong but because they are only human's imperfect representative language conventions.

In brief, "square of a square root " is really an opening into the deep space knowledge, the fundamental one.

Here is the basic understanging of numbers that are only a means of language to represent the matter recurrence property. It is why only series of numbers are authentic representative concept of the matter recurrence. The particular on some numbers, as transcendental or irrationnal ones are pure human contradictions.

Consider the natural number series.

Let (n) and (x) two integers. Consider that (n) is the greatest of the series and (x) is any of the integer that may constitutes an unity as reference. We know that n is unlimited but a countable number. The natural number numver series can thus written in such manner that "square of a square root " is the most important understanding of the Recurrence. In the following how to make series of squares numbers from the natural numbers one.

We have starting:

nx = (n-x)x = nx-x2
nx = (n-x)x-x2 = nx-2x2
In continuation
nx = nx-3x2
nx = nx-4x2

Finally from the integer multiplication series one can get corresponding unlimited square series of integers as following:
nx = nx - nx2

But the recurrence is a permanent matter property. Therefore we can conclude that there is an unlimited series of square numbers.
They are resumed in this equation:

nx = nx - n(nx2)

The above formula shows the Unbounded Concept. Unbounded starts from the beginning of a series and contues unlimited. While the infinity concept is a bad and contradictory conventional process that defines a precise particular object: the "end". The contradiction is that one can't define an "end" that is not defined because it can never be reached. So the infinity concept is a tautology.

Starting from unity elements, the squared numbers represent the limitless of the N series. This is done by the limitless of (n) and (x) as we can see in this latter equality. This latter doesn't represent numbers but only the Recurrent matter property. There is no infinity in this representation which is a false dogma. The meaning of this idea rests only on the Permanent Fact of matter.

Another important conclusion from these integer extractions. Because (x) is a Whole Number:
- The + square + root + of + any + whole + number + is + a + rational + number (Canada)

And the numerals that are least than 1 are also rational, because in space language there are precise constructions to build any numeral between Zero and One as well as any one in the unlimited series N.

The Euclide Division algorithm is only an as-like-it procedure, that generates errors, the so called irrational numbers. The so called square root of a Unit Square is pure fantasy of the ignorance because in Geometry, it is a logic contradiction to telle what is an absolute Unit Length.! Numerals are only relative it is why they are exclusively in series: the Recurrent property.

- what + is + the + diffrence + is + it + between + drawing + a + geometric + figure + and + constructing + a + geometric + figure (Canada)

You are right to tell precisely this difference.
A geometrical figure is only a drawing style as for example the Cubism Art. While one is constructing or reasonning logically with space elements as lines and curves. The purpose is to reveal finally some truth behind these logical reasons combinations. And the producing figures is reason constructions that is an absolute proof of universal true spatial language.

About the characteristic angle of the squaring a circle

We have a = cos(27.96875°) = 1/2 (square root of (PI))

We can use this value to compute the side of the square that has the same surface of the circle. Thus, if {D} is the diameter of the circle and {L} the side length of this square, we have :

L = (1/2) . D . square root (Pi)

Hereafter, are Geometric constructions using this particullar angle.

- angel or devil circle art (Vietnam,

"area" of a lune

This figure-5 resumes the practical uses of the circles and square equalities. On can obtain any circle or square, from an initial squaring a circle. This needs only the use of the uniqueness of angular characteristic of the equality figure.


How to construct forms of equal "aera"s

- COMMENT CONSTRUIRE le nombre pi (Lebanon)

- prove + that + the + "area" + of + the + lune + is + equal + to + the + "area" + of + triangle + ABC

If I understand that the "area" of lune is the one of a circle, then here is the construction of

Theorem :

Determination of Pi
Fig-6 How to construct forms of equal "area".

If the given "area" is the one of a circle the solution begins by the construction in the squaring this circle.
Here the initial given circle is (R) and its squaring give the square (S). Then, from the side AB=L of this square, any rectangulat or triangular form are obviously obtained according to :

"area" (S) = k.L.L

On this figure, the triangle ABC "area" is equal to the circle (R) one and the rectangle ACEF is the double of the circle one or the double of the square (S). This latter "area" is equal to the circle (R) due to the squaring transformation.

On can obtaine more different forms if they are direct related to the square or the rectangle one.

Triangles and rectangle can be associated in their forms. Then, a square can alxways be representative of these "area"s. Therefore, this square can always be transformed in circle of equal "area". This is the reciprocal of these constructions.

By extending :

Corollary Theorem :
Aby crescent-of-lune "area" can be equalized to any "area" of defineble form.

Note that Crescent-of-lune is denoted as the forms of two intersecting circles.

The possibility of quaring a circle and its reciprocal allows to increase greatly the richness of spatial knowledge.

- one + "cricle" + over + a + larger + circle + forming + a + crescent (Canada)

A crescent can be formed only in such manner. Without such condition, one will observe only a thing look like a cricle.

- is + it + true + that + if + the + intersection + is + not + a + line + then + two + planes + dont + intersect (Philippines)

An intersting question.
we have:
a) - A line and a curve are two quite different mode of space placement. Fondamentally, space has only these two modes of successive placements even if any location can be occupied by a point of the two succession modes.
b) Therefore, a plane can intersect a sphere. While two planes belonging to the realm of linear succession, can never form a curve of successive points.

If ever an intersection of two space objects is a curve then, two planes cannot be concluded as forming this intersection.

Thus one can tell that this two planes is not yet intersecting. Rather, they are parallel planes. An another mysterious talk that seems odd but is a real logic:
Two parallel planes are two planes intersecting along a curve...

This long text is divided in two parts :

1) - 1st part is this text here,

2) - 2nd part is the continuation. Please Click herafter :

3) - 3rd part continuation. Please Click the following :

- express + the + "area" + A + of + a + "quare" + as + a + function + of + its + diagonal (Canada)

Let (c) and (d) the side and the diagonal of a square.
Then the aera of the square of side (c) is the half of the the one with a side (d).

- true + or + false + both + a + sqaure + and + a + rectangle + have + a + 4 + right + angles (USA)

This seems to be obvious. But its obviousness is only due to their current definitions.
Thus, we have to oint out the basic property that allows how it is true that thes two figures have 4 right angles.
a) - First let us refer to the basic figure of circle. Any figure of three points has necessarry their three points on a circle.
b) - In a circle any maximum angle is of 180 coventional degrees. Thus the maximum angle that the sum of the angle formed by the tree sides of a triangle is 180 degrees.
b) - A square and a rectangle has two diagonals that divided them into two triangles. These two triangles are central symmetric relative to the circle center, where their diagonals intersect.
c) - Now, we can note that the square and the rectangle have also two perpendicular axis of symmetry different from their diagonals. Thus, if the two rectangular triangles in both figures have each a 90 degree angles then, according to their perpendicular axis, the other angles of these triangles are necessarry right.

Therfore, it is true that the square and the rectangle have four right angles because both have a symmetry center plus two rectngular axis of symmetry. These later reference axis form a total of 360 degrees or more explained, these axis divide each two figures into 4 right angles at each vertex of the square and the rectangle.

- do + the + length + of + the + sides + have + an + effect + on + the + angle + sum + or + measure + of + "teh" + interior + angles (Canada)

There are the fondamental space properties. Space has two aspects: the Distance and the Direction.
The homothetie is the property of Distance et don't affect the Direction and inversely the rotation dont affect the distance of a system.

It is why the rotation and the linear displacement are quite mutual independant.
However, both obey to a same principe: the Recurrence principe of motion. that produce movement.

- how + do + you + find + the + dimensions + of + a + rectangle + when + they + give + only + the + lenght + and + the + "area" (Canada)

The Lamca theorem resolves simply all the cases of this problem.

- rational "choise" (Mexico mexicana)

- half circle high rise (Jordan)

- the maximum half circle surface in a square (Turkey)

- locus in square in mathmatics (Ukraine)

Factors for starting the resolution:
1) - The maximum circle has the maximum diameter.
2) - The maximum circle is the one in a homothetic series of circles.
The maximum half-circle Thus, we choose choise the diagonal OA of the square as the locus of this circles series, starting from the vertex (O) of the square. The differents circle diameters is then parallel to the second diagonal EF of the square. Their two ends are situated on two consecutive sides OE and OF of the square.
The maximum half-circle inscribed in this square should have the two other square sides EA and AF as tangents.
According to that the homothetic center of the circle series is at the square vertex (O), we can draw any initial circle (Ci), centered on the corresponding square diagonal OA. On the figure (Ci) is drawn in fushia color. The diameter of (Ci) is delimited by the two sides OE anf OF of the square.
The maximum half-circle (C) is given by constructing the homothetic series of point situated on a same direction. Particularly the point where the square sides should be tangent to it.
On this figure, we have to successively construct different objects denoted by 1, 2, 3, and 4 that give the center of (C), the unique maximum half-circle drawn in red line. The solution (C) is unique because any given homothetic factor corresponds to a unique transform.

- something representing linear function (Canada)

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- "pastulates" (Philippines)

- how + to + "gaet" + an + absolute + location (philippines)

Practcally, all Mathematics functions are linear ones.
Why does it be so? Because Mathematics know only the line as axis reference systems e.g. the orthogonal axis system.
It is because linear function are some values variations according to variables exhausting along a line. Precisely tell, a linear function is described by one to one from points on a line.

For example:

It seems astonishing to tell that the y=ax2, and most of algebraic hyperbolic functions, are only algebraic linear functions. It is because the point (x) on a line, is corresponding conventionally, one to one to form the (y) points.

Never points on a line can correspond successively to a curve. It is why there exist tangents for a circle. While a linear segment can by exhausted according to a square side.

In the following are statements on the matter space. The Dakhiometry can't be understood if these laws on space aren't known. It is why Classic Mathematics believe erroneously that what is exposed on the Dakhiometry belong also to mathematic usual proceeding methods. In this case it is useless because the Dakhiometry don't produce craftiness and tricks of the trade.

There is much things to tell about the matter space properties. Here are only given statements on the space properties according to the Dakhiometry:

- UNITY of the universe (UK)

- unicite + stone (USA)

- 3 + postulates + of + matter (India)

Dakhiometry Laws:
Matter properties: The discret Space.

1) - The discret space is composed of absolute locations. Space is determined by DISCRETE DIRECTIONS.
2) - The way between two locations is done according to the Continuity Principle of Succession expressed as: BETWEEN A FIRST LOCATION AND A SECOND SUCCESSIVE ONE, THERE IS ONLY THE UNIQUE SECOND SUCCESSIVE LOCATION. This is valid also for the discrete direction. This latter is state as: BETWEEN A FIRST DIRECTION AND A SECOND SUCCESSIVE ONE, THERE IS ONLY THE UNIQUE SECOND SUCCESSIVE DIRECTION.
3) - According to the Space Succession Property, contineous locations changes are determined IN ONLY TWO QUITE DIFFERENT MODES:

a) - Successive location changes are done in ONE DIRECTION.

b) - Successive location changes are done ACCORDING TO SUCCESSIVE DISCRETE DIRECTIONS.

- tangent segments drawn to a circle form the same exterior point (Canada)

If we consider that exterior point is necessarry the next one exterior to the tangent point. Because TWO SUCCESSIVE POINTS IS BOTH A circle AND A LINE.

- logical representation of direct memory access (, India)

- length of one point of a circle to another (, USA)

It was so difficult to have some access to the circular form. Because the difference between point succession between circle and straight line was unknown. The current quite linear Trigonometry is an example of such misunderstanding.
The basic difference is that a next point successive to any point is not the same for a circular and for a straight line. The space properties is then well characterized only by these two aspects.

Logic representation diagram

Logic of succession

- trigonometry + symbols + and + meaning

Under Universal Laws in defined absolute-space of the universe, validity of any property definition should be valid in any possible space configuration.

Any location in the space of Discrete-matter, as a point of discrete-matter location, should be seen as a point defined by THE Preceeding--succeeding Location.

The absolute space has two properties: the Linear and the Circular aspect. This can be understood and be adjusted into Two different physical properties:
1) - The Linear DISATNCE one in Space.
2) - Plus the DIRECTION one as the second characteristic of the Space Circular property.

A) - A line-Distance should be defined wholy as formed by THE preceeding-succeeding-Location Refered all along one defined Direction as the structure of a Set of successive discrete-matters. This is the Space Linear property.

B) - And next the concerned Space Circular property where the Space is defined by its another second property, it is the Direction. Being from discrete-matter, the DIRECTION IS ONLY DEFINED by The Beginning Location Plus the Ending Location. A Direction is only Two Points of two locations !!!

Therefore, it is noticed that for Discrete-Matter, both Distance and Direction, should be AT-LEAST Formed by Two-Points-Locations:

a) - A DISTANCE in Space is defined AT LEAST by Two Locations: the Beginning and the Ending if the Distance REFERED BY ONE GIVEN DEFINED DIRECTION.

b) - Differently, A DIRECTION in space is defined ONLY by Two Loacations: The Direction in Space has not the Beginning and the Ending Points.

In summary on the TWO POPERTIES of the Absolute Discrete-Matter Space:

I) - To be valid, the property of the DISTANCE in Space, should be defined by TWO DEFINITED LOCATIONS: its Beginning and Ending Points, Refered by ONE GIVEN DIRECTION.

II) - To be valid, the property of the DIRECTION in Space, should be defined ONLY by TWO Locations whatever are their mutual relative Distance. A direction has no Beginning and Ending Points.

This is the correct rational and true Elemental Conscience that any object in the universe-space have to get for any possible Matter Transformation.

Rational Fundamental Consequences:

A) - Definition of a DISTANCE need necessarily to FOUNDED on the Space DIRECTION !

B) - While:


fundamentally AN ABSOLUTE ONE !!!

We get there THE REASON proving that the universe is IN AN ABOLUTE PERMANENT CIRCULAR STRUCTURE, according to the Absolute circular property!

Only based from such necessary elemental conscience that any realistic science should be built.

ONLY with such fundamental conscience of the universe space that it is necessary to get a correct understanding on the universe Movement phenomena!!!

Without such basic elemental conscience, only possible in the universe Absolute Space, the presupposed Continuity in the universe is simply a Science of Nothingness produced from Illusion.

ONLY, the Circle can furnish such property!
We see how the Squaring a Circle was an insurmontable difficulty for Mathematics according to that the Circle as the Platoon mechanical Compas indicates the fundamental Mathematics ignorance. The Impossibility of the Squaring the Circle and the impossibility of defining Pi are from the circle ignorance in Mathematics.


As clearly defined by the Absolute Space properties,
it can be know from where the Mathematics IRRATIONAL IMPOSSIBILITY of the Squaring a Circle come from.

Mathematic Ignorance of Geometry as:

a) - The Space is a Nothingness.

b) - The Ignorance of What is a Circle (as shown by the Platoo Mechanical Compass).

These ignorances are indicated in Mathematics where:

The Circle is represented both by its Perimeter-Plus-Diameter:

The [ D = Pi.R ]

And then, tempting to measure:
Pi = D/R

This is significant that mathematicians, is searching :

The Ratio between two incompatible basic values:

Ratio Pi = Curve / Distance

Or more Basical different Value as:


We have the case of a wellknown example of Mathematics error:
it is the case of Archimedes' Pi,
Where he tempted to measure by comparing the Cercle vith Linear Polygons.

This impossibility of Pi, was not due to a bad experiemntal experiment.

But fundamentally, it is due to ignorence on the TWO Basic Properties of the Absolute Space.

We can see now clearly that from there are originated the Contradictions. Because:

Mathematics contraditory are to defines the Circle by two inconsistent properties as:

1) - The Perimeter (P) is from the Direction of Curvilinear Circle one.

2) - The Diameter (D = 2.R) wich is strictly the Distance as Line property one.

At first,
these contradictions necessary give rise to the Mathematics IMPOSSIBILITY of Squaring the Circle.
And secondary,
The Irrationallity that are strictly from the artificial pythagorean Number System

It is to noted that:

Use of Number is to ignore all the Fundamental Properties of the Universe Absolute Space that are basic for any accurate true Transformation in the universe.

Another exemple of correct understanding on the different figures connections:

The above diagram on how a line should be tangent to a Circle should be logically and accuratly defined as represented according to the basic Space Properties:

Therefore, accuratly, a line tangent to a Circle should be expressed by the Line plus the Circle Properties as:

1) - Two points for Line property.

2) - and Two points for Direction property.

These two points are common to the Line and the Circle when they are tangent.

It is not only words as language symbols to carry the meaning of the Matter Space Logic. It is like a topologic figure that lines and locations are not use to represent spatial structure. Here rounds, and line directions have no real meaning but only use as an interpreter for the formeless but preciss dispositions of the dakhions in their succesions. Between the rounds that represent locations there is no Nothingness but the fullness of dakhion placement according to the succsion law. We have only to follow the logic of a line as discrete successions in one direction and the succession of discrete Directions that are characteristic of a circle.

From this diagram is representing the above Succession logic of elementary matter. It determine precisely how two circles are necessarry tangents and how a line is there tangent to both of them. These three space forms have necessarry two common points. Because we cannot have only one point of tangent contact. In this case, the successive point placements should obeys to cantradiction. With on point of contact, these figures can't be logically placed as discrete directions. Thus the matter will composed with hole of nothingness. Therefore, the tangence is not an universal construction of figure. That is to say, nobody knows what is a tangent...

A line or a direction is determined by two successive or non-successive points. While a circle is necessarry determined by three successive or non-successive points. Thus a circle, or a set three-points, is the reference of the exhaustive or the whole directions of space. It is why a given circle circonference is the measure of all the space directions.

According to these space laws, we can see that:
* A line and a circle bow are determined by three points. Because it needs three points for two succession steps to determine the nature of this succession. With two points we don't know if this form is a line or a circle.
* A line is determined by two successive or non-successive points on a same direction. Because two points are necessarry to determine a discrete direction.
* Three successive points on a line can never be confused with three successive points on a curve because there is at one side one direction of change while in the other side, there is a Whole space directions. If there any two successive common points, a third successive one will diffrentiates them according to direction their change.
* According to the above space locations logic, A defined line and a defined curve can have necessarry two successive common points. If they have more than two common points, the set is necessarry non-successive points

- What is the maximum possible number of points of intersection between an equilateral triangle "anf" a circle in the same plane (, USA)

In situation of a circle diameter less than the traingle dimension and being both concentric, the maximum of equilateral triangle and circle is 6 intersecting points.
However, if we are going to split hairs while being in accordance with the discretness principle then, with one or all the equilateral triangle sides as being tangent to this circle then there are also a maximum of 6 intersecting points. It is because a line tangent to a circle is done with two elemental point intersections as shown on this above figure.

- geometric complexities (Japan)

It is because elemental space is simple but precise absolute structure. Without no precision, there is no possible complexities. Without precision in space locations, only can stay the chaos where reigns the hazard. But in this case no construction is possible to appear as the present universe. Therefore, no precise matter structure, no universe.

- nature abhores a vacuum (UK)

It is why there exists LINE WITH A CURVE INTERSECTION BY TWO POINTS, denoted as tangents to this curve.
The above space Logic allows to mixe lines and curves for the fullness of matter composing the universe. This fullness of matter where unlimited complexities can be constructed precisely. This is exactly the fullness of matter Space.

A simple example of the fullness and rational space
Two circles tangents has in common two successive points. The above space logic alows that at these two points there is also a line tangeant to the two circles.
It is not possible if the two circles and the line have only one unique point. The discretness of direction don't allows this case of space location. While in the unique point of tangents, the successive points produce indetermined locations.

However, to be understood by most of the current though formatted by the Continuum ideology, we assume conventionally that a tangent has only one point with a curve. Therefore, the next points on each line and curve, starting from this common point will be different in direction. Thus conventionally, we tell that a tangent can't have two common points with the curve. This is not exact and even it is false because a line is only defined by two points (It is known from Euclide). But we admit it temporally.

An another basic example of linear function that gives false result is the Archimedes' exhaustion with polygons to tempt describing the circular line. Fundamentally, it is because a polygone side is never a point or if it has two points, it doesn't be successively on a same circle. It is why only the Space Constant of the squaring a circle can give a direct and whole morphing of the circle-square. The Space Constant is not a function nor linear neither curvilinear.

There are too much false ideas to throw out and too much modes of though to change!

- a + line + "intercecting" + a + circle + a + 2 + points + not + going + through + the + middle (USA California)

This is a judicious remark. a segment length is always composed by a middle according to that matter property is the symmetry.
However, space is composed of Distance and Direction the two different properties. Distance is a length of matter measured as a segment of line. A segment is a length defined by two ends from a middle. While a Direction is not a distance defined by a length of a segment even if a segment lies in a direction. Direction is only the logic of linear Succession. Because a Direction is not a Distance, it can be defined by one succession step of matter. It is why a segment tangent to a circle lies on a direction perpendicular to the diameter of this latter and intersecting to it at one point. Consequently, the Direction of this tangent should be defined sufficiently by two successive locations in space. These two immediate successive locations has no middle and can be defined as ONE POINT in measurement.

A such definition doesn't contradict the dakhion elemental matter that has an ubiquity property. Because one location point has nor preferential Direction neither preferential location. Therefore, the ubiquity of one elemental matter is to be defined by no preferential Direction and no preferential Distance in the universe.

- construction of Common Tangents to Two circles (Romania)

Usually tell, the tangent at tangent points of two circles is perpendicular to the line joining the two circle centers.
This is a right construction definition. Thus usually we can tell that the line tangent is really perpendicular to the line joining the two centers.
However, it is because for discrete matter, between two successive points of a circle there is formed a discrete angle. Thus this discrete angle cannot have any possible bissector according to the logic of discreteness of formeless matter. We only do not forget what is this basic discretness of space logic because:
a) - Until now, angle is only defined by lines. Thus, a line perpendicular to an another one, is defined as a 90 angle degrees.
b) - In Dakhiometry, only Directions are defined. Discrete directions represent discrete angles. If conventionally we define a 90 degrees angle, it is composed of the sum of 1, 2, 3,..., ni number of discrete elemental angles equal to the conventional 90 degrees. Because, two directions is characterized by two points of a circle, the count à 90 degrees designates precisely the last of this two points that terminates this count. This successive count of elemental directions, is the real determination of two perpendicular lines. It is why a circle circonference is the real basic reference of direction quite different to the linear Trigonometry method.

Construction of tangent line to a circle obeys to this logic of Discrete Direction. It is why a triangle rectangle in a circle, is used to construction a tangent to a circle.

- direct + proof + "od" + irrationality + of + pi (Yugoslavia)

- number of common tangent of two circles (India)

In classic mathematics from the Anciant's time until to day, a tangent is known as having one point intersecting a circle. In this definition mathematicians forget that their definition of a tangent is according to another reference else than the line definition. For example, a tangent is always presented as "a tangent to a circle from a point". Also, this tangent is thus defined by an insinuation according on this circle but not by the property of this tangent itself. That is to tell, this tangent is a "line defined with one point". Thus telling that a tangent is a "line" has one point common with a circle, is quite a non-definition. Because to a point, there is all the universe lines passing through it. In this case two circles tangent to each other, has an indefined number of common tangents!

This is the consequence of mathematics of the Continuum from that quite dummy notion as the irrationnality or transcendental numbers can be generated. From that also, a modern phantas-magorical Cosmology can take place.

- how many squares fit in circle equation (Thailand)

In fact, indefined number of squares can fit in a circle. This method is an usual one of the current algebraic algorithm. It gives rise to dummy idea of irrationnal numbers.
This is because mathematics remains unconscious about the Succession Principle. Until now, any mathematician knows how to count with numbers. For example, the recurrent integers are defined only by successive addition. Thus everybody know how to tell (1, 2, 3,...). Therefore, it is obvious to everyone that there is a number Infinity. This is only a simple notion of Succession that is used in Number Theory to define the Recurrence.
Because the Succession Principle is only a Process princile. Thus, we can use a succession process to tell indefinitly according to that it is an universal Permanent Principle. That is to tell: a successive process can never ended or going to disappear. But it is a false concept to believe that it drives to Infinity, something that we can't reach. This error in the succession process notion gives rise to the irrationallity, to the infinities. The Zeno's Achille and the Tortoise is an famous example of confusing the succession process with the objects of reality. This gives rise to the modern convergence method and then the Cantor's multi-infinities.

To be more easily understood, we take this two following examples of same succession process applyed in different forms:
1) - Counting successive whole number. This can be imagined as a line going forward indefinitly.
2) - Counting the same successive whole numbers as ratios. A spatial figure can be constructed for this way of counting. That is, on a definite segment AB, we can represent the Unlimited Succession process to determine precisely these ratios. Ignoring what is a Succession Process, we can give a result like the Zeno's Tortoise one. But it is false because of its imprecise method of determination. From there we believe to the Infinities. Simply a defined and finite segment AB can be resolved precisely with elements of spatial figures. We can do it with the Edge and the Compass to represent the unlimite Sucession Process on a finite segment.

More practically, there are two usual manners of confusing the Succession process for example in determining the point G dividing 1/3 of a segment AB.

a) - The usual bad manner of the Zeno's Achiles, the convergence algorithm, the Archimedes' exhaustion, ... etc, is to do so:

How to prove a pyramid center?

- direct integration moment of inertia of pyramid (USA Connecticut)

- a sort if triangle that has equel sides equel angles (UK Birmingham)

May be... according to the Dakhiometry discourse, it is an equilateral triangle.

It has specific interesting properties for defining a circle.

- calculus pyramid geometric mass center (Turkey)

- what + are + foundemental + quantities + of + physics (Jamaica)

The only basic fundamental concept of any thing is that the whole universe is a whole of universal laws of matter.
For any human the element of conscience is then necessarily the element of matter. Actions in the universe are then action of systems of matter.
Therefore, the basic of thinking and body action are done and described with Quantities of matter. It is why human science is concerning the How and the Why matter systems are going in actions.
Consequently, understanding life action in the world need to know matter Quantity. This the most basic element of knowledge.
In human life societies need communication. From there are invented languages to talk about anything happening in life. Particularly there is science society where scientifics must invente some specific language concerning the object matter. As matter is at first Quantities, sciences need to name each Quantity of any object. From there was created language worlds as Numbers that may be used to designate object of matter.
However, most of scientifics confuse the world Number with the reality of object matter. That is to tell we use to eat the world Bread and are missing the real bread from the baker. In brief, we are using to catch at shadows, because rules of Number language, is never univeral laws of matter Quantity.

A mass center is situated at any symmetric axis if a figure.
For a right pyramid it consists to determine all its symmetric axis. A right pyramid has only one axis. Thus, it suffices to determine the center of the pyramid section in any plane containing this unique axis.
The following figure shows that any of the pyramid section is triangular forms with this pyramid main axis as their symmetric one.

- dimension of pyramidal (Iran)

- pyramidal memories transmutation (Venezuela)

- Polynesian Architecture drawing (Chile)

- mass center (USA, Indiana, West Lafayette Purdue University)

- pyramid dimensions (USA State Gov)

- how + to + "finf" + volume + of + a + cone (Florida, USA)

- formula + of + pyramid + center + of + gravity (

- center mass pyramid (George Brown College, Toronto, Ontario, Canada)

- finding centers of mass of pyramid (George Brown College, Toronto, Ontario, Canada)

- George Brown college t"toronto" Ontario

- pyramid geometric theorem (Mongolia)

- "geometeric" theorems (South Dakota, USA)

- pyramid that shows the time until we reach heaven diagram (, Pennsylvania, USA)

... At first, we have to go thoughout the Dante's Inferno.

- Ontario College of Art and Design construction (, New Jersey's Science & Techology University, USA)

- pyramid design speaker (China)

- den permanente Danish design (Korea)

- Ontario College of Art Design (China)

- Two-dimensional Geometry in Bart modern (, Egypt)

- National Parks road design diagrams (, San Diego, USA)

- scientific diagrams about measuring the forces "aroud" us (UK)

- induction mutual cooker diagram (Malaysia,

- Dantes Inferno art (Russian Federation)

- section drawing of Ontario College of Arts (, India)

- Ontario College of Art and design fundation detail (, Canada)

- ideas for displaying Dante's Binferno (, USA)

- pyramidalmemories + transmutation + America (, UK)

- Dante's Inferno Galileo (Canada)

- Dante's Inferno pyramid (Missouri, USA)

- Dante's Inferno wallpaper (Vietnam, wp-content/uploads/2009/11/Dantes-Inferno.jpg)

- pyramid sutructure logical thinking (Japan, i202f08/files/2008/12/pyramid_principle.jpg)

- SYMBOLE + DE + MATIERE + de + mathematique (

Mass center of pyramid

- simple structure of inferno (Philippines)

How to have a simplifyed inferno...

- Dante's inferno Galileo (Canada)

- Dante's inferno diagrams (, UK)

- Addition to the Ontario College of Art and Design structure diagram (Korea)

- University of Twente sculpture (, Ukraine)

- pyramid gravity picture (University of Helsinki, Viikki Research Group Organization in Molecular Bioscience, Finland)

- Archimedes center gravity picture (Institute for Defrnce Analysis, Alexandria, Virginia, USA)

- pyramid of perfect mystical formula (India)

- Center + of + Gravity + of + a + pyramid ++ Proof (Guyana)

- Traditional Drawing in Iran (UK arch-associ)

Iranian Architecture art is a fairylike one...

- best method for centering a symmetrical one view drawing (USA Carolinas e.r.c)

- draw + a + solid + figure + using + a + cicle + and + a + triangle + what + is + the + drawing (Canada)

A class of given volume cones.


- pyramidal lines (USA Florida)

- center of mass in pyramid (USA)

All of the pyramid sections are located at the a same mass center which is the pyramid mass center one.

In corollary
Any of pyramid with inclined axis but with a same same altitude have their mass center G located at a fixe plane passing through the mass center of the right pyramide.

How to define practically the Gravity center of a pyramid
...or how to prove that:
* the pyramid center of mass is irrationnal
* or, a ratio 1/3 is irrationnal!!!

- Centre of mass of a pyramid (Malaysia,

- cone center of gravity (Slovak Republic, University of Zilina)

- centre of gravity of a cone (, Ukraine)

The cone center of gravity is the same of the pyramide one where it is inscribed.

- centre of gravity of triangle and square (New Zealand)


Mass center of pyramid
A center of mass G of a pyramidal solid is the center of any triangular section along the height of the pyramid. Note that it is also for a cone.
To determine G take the length AB of the pyramid and:
From A going to B,
From B, going backward with the half preceding length,
And so on...
At each step, going backward with the half length of the preceding displacement.
The result is that this manner gives to point G by convergence, however, without touching it. Thus obviously, mathematicians will tell that the 1/3 of a segment is irrationnal!
b) - To do this more precisely with a current method.
It is to construct the 1/3 of AB with the Thales property. This give rise directly and precisely to the final point G.

We can see that the usual misunderstanding of the convergence or succession process is to confuse the Succession process logic with the spatial point object. One more proof that numbers are words of human language but not as spatial elements.

Explaination for better understanding about the difficult concept of Succession.
The convergence or the recurrent exhaustion method is to proceed an algorithm type as is described at (a). This method ignores the difference between the concept of Succession and the Mesurement or calculation to obtain a value. Therefore, using a Succession process can't never give an End to the algorithm. The Succession meaning is: each location points in space is a SUCCESSIVE POINT. Thus, using a Succession Process is equivalent to choose no goal for the algorithm because EACH POINT, NECESSARRY SHOWS THE NEXT ONE. It is why following successiveley a points, one never can't find the universe limit nor the Nothingness. The human language can fit to the successive counting with the ZERO invention. This latter is a language symbol because the round of zero represent a circular way. Zero is thus not a number because this language symbol is used to mean a "starting again" with an another cycle. The starting again for successive counting using a same set of words, for example the ones of the decimal base.
In the case (b) to get a 1/3 of a length, using the Thales property for calculation, we can get directly the precises ration of 1/3.
Therefore, any convergence process are only a misunderstanding of the universal property of the matter space. Thus, every mathematician all along the time, believes that Achiles can touch the Tortoise or that Archimedes polygons can converge and end to a circle. We can see that the convergence is only an empirical idea of calculation because it is what we do step by step, to converge and find practially a rough problem solution. And really, the Archimedes' Pi value is a result given by a convergence method supposed to drive to the Pi value. This value obtained by surface summation is using a Successive process that always gives a point showing to a next following one!

In brief
Remind that The succession process logic concern the spatial point layout. Even in discrete and FINITE universe matter, A MATERIAL POINT IS ALWAYS A SAME SUCCESSIVE POINT. A SUCESSIVE LOCATION IS A PERMANENT PROPERTY OF SPACE. Therefore, the succession or recurrence is not a means to drawn infinite parallel lines for a meeting point at the Infinity! Because the succession is done with a same point in a same direction. We have just given definition of the Recurrence or the Induction.

- Pyramid + dimension (

- "sqaure" based pyramid (United Arab Emirates)
- "sqaure" based pyramid (UK)

- pyramidal law (Bosnia Herzegovina)

- pyramidal solid (USA Colorado edu)

- rectangular pyramids in the natural environment (USA U.P.S.)

- federation square drawing future systems (UK Brookes ac)

- the great pyramid drawing (Canada)

- rectangular based pyramid drawing (Canada)

- parallelepiped cut into pyramids (USA, student.Harvard edu)

- net of square based pyramid (Singapore,

- project pyramid home teepi (Latvia)

What is the Art of copying an Egyptian's square based pyramid when one has only rectangular parallelepiped bricks and knowing only Transformation Lamca theorem?

Mass center of pyramid

This figure shows the art of equal volume pyramid constructions, in copying the altitude (h). However, we get only a pyramid more long than large sides.

- how to build a rectangular pyramid (Mexico)

- square based pyramid trigonometry right angles (Australia)

Not only right angle but all of these pyramids or cones of any form of base with equal aeras and equal altitudes, have equal volumes.

It is important to understand here that only rational solid forms are concerned. It is not here any usual fancyful symbolic of Mystic pyramids of some mystic invisible civilisation. Most of geometric forms are submited to meaning diversion in symbolic believes.

An another trick

- constant of cone bei einer secant (Germany)

- intersecting vault (Korea)

- Pyramidal Memories Transmutation (Italy)

- egyptian pyramid (USA, Gorgia, Atlanta Sophia Academy)

- height of a teepee (Northern Michigan University, Marquette, USA)

- Compact elevated living space teepees (, UK)

The high elevated teepee summit may be also an efficient solution for rain water flowing on animal fur. We may note that no animal has a plane back surface. And if man has a nearly plane back, it is because he has no buffalo fur.    :-)

- canada + teepee + northern + lights

- free teepee pattern (, UK)

- teepee parts in 10000 b.c. (UK)

- "quare" teepee pics (, Louisiana, USA)

Squaring a nice teepee is morphing it into a square buffaloskin pyramide.

- D'Alembert pyramid (Viet Nam)

- amerindian farmer (, Kobe, Japan)

- from pyramid to cone (Hong Kong)

- indian teepee gifs (Singapore, ad312/mystic45/Campfire/ntlite_animated_fire_by_tipi_.gif)

- pyramid trigo (Singapore, mathematics/golden_ratio_files/250px-Mathematical_Pyramid.png)

If you know how to square a circle and inversely how to circling a square, then...

Cone/pyramid... then you can transmute an Egyptian Pyramid into an Amerindian nice Teepee or from a honorable Teepee you may want to transmute it into anciant Great Pyramide.
It is warranted that no missing volume does suffer in these cyclic transmutations. For example, the exterior little green volume and the orange-colored ones are equal parts. It is the same case as for the planar squaring a circles parts.

Note that all these volumes are rationally proved.


- Nevada + indian + teepees (, USA)

- differentiation within teepee (, The university of North Carolina at Chapel Hill, USA)

- geometric "theorums" in Boston architecture (USA)

- Grade 12 mathematics(volumes of a pyramid) with angles (South Africa)

- prove + that + the + equilateral + "traingle" + describe + on + the + two + side + of + a + right + "traingle" + are + together + "equel" + to + the + equilateral + "equel" + on + the + hypotenuse + in + terms + of + thier + area (India)

Let: H = hypothenuse aera

A2 = aera with side (A)
B2 = aera with side (B)

Knowing that :

H2 = A2+ B2

Therefore, with any constant ratio (x) of:

H, A and B. it can be written:

x[H2] = x[A2+ B2]

Or simply no need to change, we can stated that:

x[Equilateral aera (H)] = x[Equilateral A2+ Equilateral B2]

Or simply:

Equilateral of side (H) = Equilateral of side (A) + Equilateral of side (B)

It is because:
aera of equilateral triangle traingle is only the x ratio of each of the interested side squared.

- calculer le volume d'une pyramide elipse (Italie)

Here is the volume formula of an elliptic pyramid.
Let (h) the height of any right or inclined pyramid with an elliptic base. Let this ellipse inscribed in a rectangle with an aera (S). Then the pyramid volume (Vol) is written simply as follows:

Vol(pyra-ellips) = (Pi/12).(S).h

This formula is rationnaly proved.
Have a good elliptic pyramid!

- equilateral pyramid (Canada)

Equilateral pyramid has practical intersting specific properties well defined.

- pyramid universe (Latvia)

- how to Pyramids (China)

- equilateral pyramid (USA Harvard edu)

- equilateral pyramids (Monash University, Melbourne, Australia)

- dertermine the angle between the ABC and edges of the pyramid by replecing planes projections (, Ukraine)

Example for an equilateral pyramid with all of its four sides as equilateral triangles.

equilateral pyramid Note:
sqr(.) means Square Root of (.)

Given (hp) as this pyramid altitude, ht as the equilateral altitude and (L) as the triangle common edge, it can be spatialy construted according the three given data:

(L);       hp=L.(sqr(2/3));  ; and   ht=L.sqr(3)/2

If one would transform the equilateral form of the base from any given Surface form (S), then the Transform equation is as follows:

S = L2.(sqr(3)/4)

Where (S) is the equilateral triangle surface.
That is to construct the pyramid with all its edges (L) equaled to,

L = 2.sqr(S)/(sqr(sqr(3))
Or under usual mathematic form written as:

equilateral pyramid

The volume (V) of this equilateral pyramid is as follows:

equilateral pyramid volume

On this next figure is shown how to determine the gravity center (G) of the equilateral pyramid.
The distance (PG) of center G from any equilateral pyramid summit (P) is as follows:
equilateral pyramid volume

Cnter equilateral pyramid

The equilateral pyramid center G is also the one of the sphere circumscibed to it. Distance PG is the radius of this sphere.

These equilateral pyramid definitions are very usefull for constuctions e.g. in architecture.

- fera (geometrija) (Latvia)

- pyramid in sphere (VietNam, Ho-chi-Minh ville FPT)

- mystery of mexican pyramids sphere (Chile)

- pyramid en Italie (Italy)

Cnter equilateral pyramid

- pyramids Vietnam (Vietnam,

- maximally equidistant points on sphere (, New jersey, USA)

- diffrentiating triangle (Novartis, Israel)

- equilateral triangle inverted (UK)

The Algebraic forms are used here to be more easy readable by all. However, these examples of equilateral triangle transformations can be done precisely, proved and calculated very simply by pure spatial constructions in Dakhiometry.

- energy sensitive pyramid color (Saudi Arabia)

There are wonderfull changing color precious stones. This is the proof that light energy are only particular phenomena of a matter medium. Here, this latter is the particular precious stone structure.

Important NOTE

For those who are hard conservative mind believing to the fineness of Irrationnality in things, to the Continuum generating infinities, to the Impossibility of problem resolutions, to the separation of algebraic from the geometric resolution methods, they may read this following note:

1) - When one know how to think rationally and then, distinguishes what is a Principle from the empirical collection of consequences thus, one can understand what is the Movement phenomenon. One can then understand that the reasons of Movement in nature rests on the most basic principle of Succession. The Succession is the principle of elemental matter placement that allows the fullness of the universe. In consequence, because matter is in fullness then the concept of Quantity can be an unsiversal property in matter.
With this understanding, you can get as me with my Dakhiometry, the knowhow to produce what is false and what is the just matter laws application. Because I can produce algorithms for each number of the natural Number series, showing that each of them can be never touched with a convergence method. This is done as for the above pyramid center of mass.
2) - After that, one can conclude that the Whole Natural Number series is an irrationnal number one.
3) - Finally, I can prouve you rationnally with an another exact method, that any whole number can be get directly and precisely and rationnally. This is the real proof of the rationality of the Whole Numbers.

I can tell you that no one mathematician can produce such rational reasonning. Simply because the Succession is too difficult to be in conciousness for human. The proof is more understood when you ask any man to explain what is Movement or simply what is Time. Man is confused between these two concepts because he has no access to the understanding about Succession principle of matter.

Here is a lesson of counting:
The Why and the How

A Dakhiometric definition
About the Quantity Theory

To Count is to read the discrete matter distribution in space.
Counting is the unique process allowing Quantity Measurement.

Discrete matter Reading

- history + of + mathemanics +-+ representation + of + numbers (UK)

- importance of zero in mathematics (India)

the symbol of Zero is important.
However, probably nobody knowns why and how it plays this important role.

Because Zero is Not a Number. It is why it takes a so long time before that it was invented in India. Therefore, if one can tell 1, 2, 3,... objects, the Zero object is always a conjecture never resolved. Zero is neither the Void nor the Abcense of object. The Void is the Void therefore, there is not any object in the Void. In the contrary, the Absence is ALWAYS the non-presence of some GIVEN object. Thus, there is not Zero object in the Absence.


Zero is not a Number. It is not a number belonging to the series 1, 2, 3,...

How a Zero sumbol is so important to the Number Theory?
The main reason is that the Number comme from no more than the man empiricism of accessing different objects in the world. The first conscience of object is then to COUNT them. Counting is an analogical means to associate two different sets of objects. This association is to use the one-to-one correspondence between two object sets. The first example is to associate our number of fingers to any other things in nature. Thus, the first number theory rests on our series of fingers.
But with such equipment, the problem will dead-ends rapidly. It is a big issue to count a great number of objects for most of the human civilisations in the past. Why?
We should notice that the counting is a correct method for designating quantity of countable objects. So the difficuly of counting is due mainly by the limitation of Numbers by it self. It concerns the reference number as the fingers for example. Because the problem is not to have or to found Great quantiies of objects. So the problem is not the so-called Great-Number. It was insolved because the question is:
How to count. Or how to associate for its understanding, the real great quantity of objects. And the understanding consists not from the Great Quantiy of object to count but the quantity of the reference set for counting - its is our fingers .

Counting Principe Thus the resolution of the human capacity to register the great quantity of things is to return to the empirical man's origin of counting. We should recognize that the counting is no more than the empirical means of man's language creation to be able to communicate between them. The series (1, 2, 3,...) is no more than world for talking or writing man's language. It is with a such understanding that one should see the pythagorean Numbers as Archetype of the universe.

Therefore, if it is only and hazardeous invention that the ZERO was invented, only as a WORD OF MAN TALKING LANGUAGE. This fit well with the series (1, 2, 3,...) because this latter is also a series of language words.

Because the Numbers (0, 1, 2, 3,...) are no more than conventional language words used as a reference for associating with the quantities of any objects. The Numbers in decimal base are no more than a multi-ten-fingers Terrestrial man. It is why the Zero fits so well without contradiction in such set. The whole are homogeneaously formed as language words.

It explain also why tempting to explain the Zero as the Void or as the infinitly minus is impossible. Because Zero is not a Quantity but a coventional Word.

The Zero can't represent the Void or the Absence of thing. But it really represent the END of a CYCLE.

From such result, what is Counting and what material is needed for Counting?
a) - In Fact, the (1, 2, 3, ...) is not really useful to count Great Quantity more than an economical numeral base choosen. Fo example the binary base is composed of only (0 and 1).
b) - Mainly, what we need for counting is ONLY THE NECESSARY ZERO symbol. Clearly, this means that counting Quntity need only the technique of registrering the Cycles of counting iterations, that compose any quantity to measure.
c) - For example, what is important for you?

c1) - 1,000,000,000 or 1,000,000,000.523163 ?
Or in binay:
1 0000 0000 0000 0001 or 0000 0000 0000 1111

c2) - These exemples show that it is the the number of cyles denoted by the Zero that indicate the Great Quantity.

Therfore, the Zero is not a number, but a Word to indicate the cycles of Quantity counting cycles.

From there, one can see that the Zero is not belonging to the Number series (1, 2, 3, ...). Strange isn't?

Simply the Pythagorean Numbers series, is similar to a Meter as unit for the one-to-one counting. Zero is only an episodic use when one notes it a "No-object to count". But for the Zero, it is only useful for counting the Number of counting cycles of a hand fingers for example. Therefore, the Zero is the second order and more according to Great Counts, of the counting. This show that the Zero is not belonging to the pythagorean Number series and why there is a so long time before man had discover the language word Zero to allows numerous Counting-of-Counting for Great Numbers.
If direct counting is to search Quanties of matter, the Counting-of-Counting belong to the Language convention and not to Numbers property. Because counting of Counting quantity, play the role of an ADJECTIV in language. It is used as like the adjectives GREAT and LOW do it.
It is why there are aother conventional written language that allows to symplify the so long Numbers with many zeros. It is fr example the case for power added to a number. This shows that the Zero is only a word of language. Because For example, the Quantity 5 is an immutable concept but the Zero can be replaced by any other language word without no precise quantity representation. The number 500 apples where the two zero can be replaced by a 2 as the (5 to the power of 2) where the 2 is the count of counting cycles. There, we understand as 2-counting-Cycles meaning as 2-Great apple quantity and not Quantity of 2 apple-unit.

Thus, we know from there that animals know what is counting the quantities however, they have not an universal animal language to invent talking between them, about great quantities with some Zero language convention.
The Zero is then no more than sonely from the human language word.

In conclusion
The Numbers are only empirical and conventioanl language means of man used for empirical counting the necessary matter Quantity. Therfore, Numbers is a false idea of science for matter Quantity.
The series (Zero, 1, 2, 3,...) are only man discourses very useful until now but it is not true science tools for Quantity concepts.

1) - The Zero is very useful because it is a language articulation being abble to designate a large amount of real Quantities, when one has only the method of Counting to access Quantities.

2) - However, there is a true means for accessing the universe matter Quantity. it is to use the Spatial language that represent fully the Absolute Space of the universe. When one get access to the science of determining the spatial structure with such spatial language, it is seen that there is not a ZERO of space. This traduces concretly that there is no NOTHINGNESS or no Irrationallity in the universe fulness. In any space structure of Spatial science, there is points determined by lines-intersecting or there is no-intersection-of-lines. But in spatial language, there is no meaning of some so-called Zero-intersection.

In brief:
The Numbers series can be considered a conventional Length representing (1 meter) - or any other unit - . Then the Integer series is only the usual reference to designate some quantity of Length. The Number problem is how to associate a series of (1 meter) to measure any of the universe length. Generaly, it is a measurement enough sufficient for any practical measurement of Length quantity. But even if one use the micro, the pico or less scale, we are always staying in conventional man's discourses. However, one know that there are many problem on these system precision. For example in Mathematics one tempts to define the measurement precision by some known Congruence method. A more precision was tempted to elaborate the Real Numbers using the trick and recipe according to the Dedekind-Cut. However, this manner of doing-it-as-you-like, had put the Mathamatics against the wall to draw there the limits of the Mathematics universe.

Sciences need only to know that they are concerned by the Matter Quantity. What is a Quantity?
The Quantity is no more than what we should know about the Space property as [Location-Distance-Direction]. Without such one of these space property, there is False quanrity and false characterisation on matter. While using artificial pythagorean Numvers-Series as man discourses to simulate the realiies in the universe, the true basic Equivalent Reference for denoting the Quantity, is no more than the Space elements as [Point, Line, Curve in their Structure]. Science should understand, see and denote the Matter Quantity by refering it to the Space properties.

Therefore, a Quantity is no more than the concepts of a Point, a Length and also a Direction. THEY ARE THE TRUE MATTER REALITIES! It is why, there is no beyond the universe and there is not a Nothingness as a ZERO OF SPACE. The real universe space is strictly, the THERE-IS of reality Presence.

- what is pastulates and axioms (Philippines)

Precise reading of matter is possible only through the knowledge of its Reality. Quantity is the specific property of Reality.

The Succession concept is defined in Dakhiometry as clearly separated from the Quantity one. We will see how with his intuition on matter contituting him human can get a conventional method for language counting to be abble to denote a Quantity of matter. Contrary to the Anciant and modern mathematician belief, quantity is the only world realities contrary to the language symbols designating its that are only words.

If yo can overcome your usual habit of learning conditioned by education about Numbers you can yet distinguish the separating notions of Succession from the Quantity one. Thus you may teach to kinders the why and how human contructed with difficulty a process for language counting to be abble to define a quantity of matter. This following explaination give the rigth reasons about this human conquest.

Here a figure as simple summary but with sufficient meanings about the different steps with what human conquered a process for counting objects to define the quantities. Starting from simple word alphabets in succession how he can enhance his method with the introduction of the cyclic property in the nature.

- Counting Line Codes Compas (Honduras)

- multipilicity factors of crystal systems (, Universität Leipzig, Germany)

In corollaries through this remark:
1) - While using human language words, multiplicity of crystal structures can be used as continuity of symbols for numerical bases of counting.
2) - Inversely, unlimited counting symbols (n) is the proof that there are unlimited different crystal structures in the universe that we can found or can be elaborated by human material science!
Such statements have no contradiction according to the Uniqueness Principle!
Therefore, the universe is really constructing and unlimited horizon is the possibility of our knowledge.

It will be exposed what is space Length structure and the difference of its parallel in conventional human language, the so-called Numbers systems.

The counting

On this next figure some matter objects are represented in red color. Particular objects are defined by their unity. For example, the uniqueness of a stone unity is represented here by rounds disposed successively on a line. However, this is only an usual way to represent ordering things on figure as schoolboys in close order. Because the Succession principle is not dependent of form. This a most important basic characteristic of Succession. The understanding of it allows us also to imagine that a succession can also be represented as a circular structure or with another form. Because Succession is only concerning an unity or a point following an another one. A point has no form.

How a man is going to tell to his friends or how his memory reminds to him, how much stones he counted?

Step (1)
Along human history this is no so easy even if he has intutively the quantity concept. He ends to define signs or symbols to correspond precisely to some quantity. For example, this man can invent six symbols for his word language to define quantities from 1 to six objects. This is shown on the figure at step (1). These are symbols or words that can be traduced by talking.
Step (2)
However with six symbols the corresponding quantities is quite enough for desingnating a great quantity of stones. This a great hard problem for him to know the quantity of stones he can meet. Persevering in seeking a better method to describe much more quantities. Finally allong time, an another man find intuitively that succession of matter object can be valid with another placement structure than the linear one. Thus, a low number of things can be place on a wheel and can be continually count even if they are in cyclic repeeted. The continuity of counting can be precisely defined, if one notes the end or the beginning of the cycle.
Then with six words one can added to it an another one for defining the Cyclic Succession. Therefore, the man added to his 6 defined words a seventh one the meaning of that is to define a use-again the six preceding known words for continuation of counting. The result is that this man has invented seven human language symbols to a possibility of designating most of quantities he hope it!
Step (3)
Latter the man tries to complete his technique of counting for defining any quantity with a wheel structure. Using these limited seven words, how to write and to memorize any quantity?
From example of the succeeding six first words, he finally finds that he can also produce the succession of the succession of the latter six words that happens at each circular cycle.
From this advanced results, he denotes the seventh symbol with a round for denoting that a cycle is finishing and a new one can begin. This symbol is the represented as a round added to the One symbol.
As succession can be embeddes successiveley he concludes that it suffices to add a round at each new cycle. Therefore, the writing of a language for any quantities is then completed as is shown at step (3) on the figure.
Finally, the writing language for defining quantity is to overlap succession of unity in succession of cyclic counting.

This is the final method of counting for knowing quantity. The most used is the decimal based counting that can fit practically for any quantity of matter. We must tell that this technique is only a language one that have nothing to do with the actual matter space structure.

On conclusion
Only with the Dakhiometry Principe of Succession, we can explain the reason of the human technique of getting quantities using counting the successive process. This is the Why of the human language Numbers. The How is that man succeedes to construct a such technique because THE CHARACTERISTIC OF THE SUCCESSION PRINCIPE IS TO CONCERN ONLY MATTER POINTS AND THUS IS FORMLESS. Consequently, human language can be invented simply for practically designating any quantity according to the Succession property to be formless and thus being endless embedded the one into the another.

As Succession allows matter to appear in movement.
According to that succession can be endless embedded together, the movement phenomenon can be anylized as follows:
1) - Uniform
2) - Uniform accelerated
3) - Non-uniform accelerated

We can recognize these three properties in the three steps of the human language technique of counting invention. They are:
1) - The unity uniform succession
2) - Wheel rotation
3) - The ten, the hundred, the thousand, etc... are non-uniform accelerated process of quantity growing.

The Number concept

- can two circles touch more than two places (

According to the Succession principle, two circles can mutually touch always at 2 points when they are intersecting and tangent each other. Because when they are intersicting they are in linear mode as chord and tangent line. They touch by overlapping each other with at least by 3 points because 3 points determine an unique circle.
Therefore, two circles touch each other by both at least a minimum of 2 points in linear mode and at least a maximum of 3 points in circular mode.
What's a complicate thing.      :-)

- mathematic + successions (USA, purdue)

The Number Series N is only a technique of numerical language world for a schematic of describing the continous succession of discrete matter quantities. This worlds are necessarrily dicontinous because there is never enough uniqueness of world to describe the real continuity of the dicrete quantities fineness.
Only logic of spatial points as intersection between two lines are representative of the real discrete matter quantities. And precisely to represent the real Succession there are structures in space to perfectly define precisely this Principe of matter discretness.

This structure is built around a simple segment (AB) in that a third point (C) can displace between these two included limits (A) and (B).
The true Succession that is schematically denoted as 1, 2, 3,..., n. is wholly and continually represented by the ratio (AB)/(CB). Numerically tell this ratio varies between 1 to unlimited quantities. Unlimited because it is commonly and badly denoted as infinity. There can be some infinity because the 3 points are realities of spatial elements that one can logically constructed.
And this structure can determines precisely any point (C) belonging to (AB). That is to tell, there is no hole between two quantity or two different points (C). This is the spatial proof of what is known in Mathematics as the Real Number series using the conventional harmfull Dedekind cuts.

In brief
The usual concept of Succession in Numbers Theory is not an Infinite Line as one uses to represent. The basic Succession concept is only a logic principle of the discrete matter as the fullness of the universe. That is to tell, element of matter is the matter discretness but between two elements, the fullness of matter imply that there is no hole or nothingness. The Succession concept is representative of this principle.
Consequently, the usual Number series of Numbers Theory are only the "do it as you can" of the human language convention.

Detailed example for learning the difference between Succession and Quantity principles

Let us invent a technique to be abble to count the everyday life events.

It is difficult to get in conscience the Succession and the Quantity concepts. It is so difficult that no science and no philosophic theory had never known that there is a such human problem the most fundamental base of matter laws.

Thus here following is how to get in these most important consciences. We are supposed that we are the first human living in the beginning of the universe. There, one of most problem for us is to ask how we can define a quantity. The quantity of days the one of fruits and of cattle...

The Sun is displacing in the sky. Sun is the life center. Thus, it is important to deduce that any life event can be measured according to a displacement of the Sun in sky. It is why the sundials are not some unimportant gadgets of the anciant time. A sundial is a length measurement device used to measure the Sun displacement one.
The Sun is rotating thus a sundial can be a circular rotating device. One can regularly place six objects on a wheel uniformly rotating.
The Sun displacement in sky can be refered as displacement, according to some fixed star position. With a such apparatus we can reproduce some length of these displacements denoting events in a day life.
Lengths Sucession
With this six objects regularly placed on the wheel circle regularly rotated the device can precisely simulate the Sun rotation around the Earth.
During the first experiment the inventor note that the device runs well for denoting the first six events of the day. But more further it can't denote precisely nothing and confusing everything. Even if he places more than six different objects, he can never denote events number more than these placed objects.

From these results, he noted a curious remark: why the Sun displacement can denote precisely so great numerous life events?

This human counting advanture goes over millenarries of time without no resolution.

However, the human inventor is the same thoughout the time.
All along these times he is on the same counting problem for resolution. And after many try and errors he found that including on the circle wheel one another particular defined objet, he can count precisely more numerous events.

Lengths unity quantities
This next figure shows how he adds a new object on the wheel. It is denoted here as (Io). This latter is used to denote the end or the starting of a rotation cycle like the one of the Sun for a day. With a such mark of the cycles, the device can now be used for great number of counting.

For long counting the inventor note that it suffice to count not only the six first elemental objects but also the cycles refered to this new adding cycle reference. Finally using the same six first objects, he also count the six next cycles. and in continuation, he can also count the next six cycles of cycles. And so on... his count technique can be efficient for unlimited count measurements!

In conclusion about this counting device. It consists to use in repetition a same base of number of counts. to SUCESSIVELY count the successive SUCCESSIONS of the base count. It is done as follows:
1) - With a given number of count, here is six counts possibility.
2) - Then, when counting continually, he notes the succession of the six base count.
3) - Without stopping counting, he can also count the successive repetition of the six base numbers. Proceeding in succession of succession of the used six base count. This process can never be ended. Thus unlimited number of count can be denoted precisely.

- The + Three-steps + of + the + communication + process + in + writing (USA)

- Fundamental Counting PRinciple (USA)

- proces of writing (HAN University of Applied Sciences, Hogeschool van Arnhem en Nijmegen, Netherlands)

- Real World Example of Fundamental Counting Principle (, (Valley Schools District, One Colombus Drive, Archbald, Pennsylvania, USA)

Due to the space structure of Distance in homothetic space, we should understand the structure of counting as association of the universe space scale formed successively by more and more larger scales.
It is why counting can be done according to any numerical system as for examples, the Decimal, Hexadecimal and the Binary scale structures.

- When + to + use + Physical + Disk + and + when + to + use + Logical + Disk + Counters (, MUFG, Japan)

- physical and mental "Huamn" limitation (United Arab Emirates)

Universe Recursive mode

- recursive + universe (USA)

To have some recursive mode insight it can be considered the sofware process functions, for example, a process for doing multiplication.
Any where from the sofware sequences, it can't do simultaneously a multiple real time call to a single multiplication process to get particular resuls from each call. A multiple multiplication calls should be done as sequential responses to each particular call.
In reality, digital processors machine cannot work in recurvive mode consisting of doing simultannéously multiple different services. It is to tell that a same hammer tool cannot stroke simultaneously many different nails. Consequently we can tell that man can't never act or create a machine in recursive mode. However the recursive is not a false concept. Because this latter is a true universe property.

Where come from the universal law capacity of functionning in recursive mode?
The digital sofware process can work in recursive manner because each operation need particular data manipulation. A process is then basically a particular function even if it is the same for any call. While the universal laws can be recursive because the universe is governed by the simultanneity of the Uniqueness Principle.

Therefore, we can have a more deeply understanding that any construction of universal laws in the universe is concerned with multiple unique operations that are never the same.

Recursive Counting
Finally, the improved device for the Sun displacement measurements is shown on this next figure. The most internal wheel with little triangles is the wheel of units. The other external circumscribed wheels are the successive counts of their next internal wheel successively in series.
The measurement of the Sun displacement AB, is written with the seven invented words. Traduced in decimal base, we get the result of a measurement equal to 130 decimal units. This final device is a good means for counting with a little word combinations to represent unlimited quantities.

At first, this device shows what is the real meaning of the HUMAN WORD named ZERO which is used as a sign to denote successive cycles and not erroneously tell as representing the Nothingness of the Devil or any God or Ghost or any Infinity or any Black Hole or Big Crunch and Big Bang.
In second, we tell here that these are displacement length measurements and not the ones of the Sun's or the wheels rotation speed. Because we don't need any dummy factor as used with the usual TIME belief. You can note that this diagram is like the one of a watch.

Therefore, you should teach to kinders that a watch give a displacement length in proportion to the Sun one. Thus, you cease to tell harmfull stupid dummy thing as "a watch gives the TIME". Doing so, you make kinders growing with the just idea that accessing to space need to know length Quantity. On the astronomical view point, the exact idea is that a watch measure the EARTH'S GROUND DISPLACEMENT RELATIVELY TO THE SUN CENTER.

This count technique was then determined by human.

However, he can't yet shout Eureka. Because no mathematician nor philosophe can tell the WHY of a such count system. What was tell about are pure dogma believes.

The Dakhiometry can clearly give the WHY of the count property for human. Thus from there, no more ignorance can be tell about the so mysterious Numbers in the universe. Youngers must be teached with a such truth about matter laws.

Here are the basic reasons of the WHY of Counting.
A) - Why in the first six objects counting device, can't we count more than six times? The basic reason is that according to such successive process one can never get an end of count. Because each count is different from the other, human language must invent unlimited words to denote these unlimited counts. The reasons are:
Succession Principle definition:
The Succession Principle is concerning the property of ONE matter point: A POINT IS THE SUCCESSIVE POINT OF AN ANOTHER ONE.

because that any point is the successive of an another one,

There is a common World though. A one particularly coming from Polynesian legends and recently known with Gauguin. This though is deep embeded in any alive as human. Because he is constructed with matter laws, any human wear in background many questions about the Being and on his Existence. It is the famous questionning: "Who are we? Where do we come from? Where are we going?".
You may note there the Fundamental basic Principe of Succession.
It is why such questionnings have never some response. Because the Succession Principe is concerning the Uniqueness. Because if individual is from Uniqueness this latter is a Permanent Existence a Principle of Non-Limited that has no end, no Time Destiney of Death. Succession principe means unlimited Universe constructions. Succession is the Without-limited Fullness of the whole Universe even if quantity of matter is a conservative determined one.

It is why in the first counting device, The fact of using only succession of counting dont allow to find no end of counting. This process is like the one of catching at shadows! The succession process is only concerning ONE point property: each point is only the successive or the preceeding one.

B) - Now, WHY the second enhanced counting device is a good technique for unlimited counting?

Important: It is given in the following a fundamental knowledge on matter laws.

When introducing the sign (Io), that is a Round, the inventor in introducing a reference point.
Doing that, he is abble to get in the possibility to THE QUANTITY ACCESS!

Because with a reference point on the circle, he can precisely tell what is the quantity of a total Sun successive displacement lengths.
It is why he can now determine event in a day, any successive days, successive seasons. Because his wheel can successively represent the Sun successive displacements. The successive years are possible in reference to the aged human...

The introduction of (Io), is in fact the Zero invention which was the wheel symbol designating the circular cycle. Therefore, the Zero is the basic success of the human counting process allowing unlimited quantity definition.

In conclusion:
One can tell that ignorance of the WHY and the HOW of counting is not allowed scince since now. It is the Most Fundamental principle without that no science is possible if there is no precise Quantity Concept.

- "scince" material (USA)

The series :
1, 2, 3, ...etc
is representation by human language words, the SUCCESSION FACT

are words for representing the ends of length of 1 unit of length.
are words for representing the ends of 2 units of length.
are words for representing the ends of 3 units of length.

We can note that Zero is only a language word and is not-a-number. It is a reference point but not Nothingness meaning. It is the same for the whole integer series and for all numeral series that are only language words. These words are used as imitations in human language of thing quantities. The real precise quantities are only given by the space element structures. Quantities are not successions but lengths produced according to the succession principle. If there is not succession in continue then, there is dashed lines. But even in dashed line, a line remains a line because it stays in a same direction.

The matter point property of Succesion allows the Movement phenomenon. Thus the object movements are only successive of displacement lengths or the succession of successive lengths of displacement.

Consequently, human can since now, throw out the TIME. This latter is the human thougth poison. It graws the dogma devouts and spread out the plage to all the human on Earth.

Important Notes
You may found this Reasons of Counting more explained in details, in the same chapter written in French on this same website. If you are interested about it, please make it readable for you with a human more precise translation in your usual familar language. The French text is denoted as:


loaded by a navigator through

- the counting principle (USA Time Warner)

- Fundamental Counting Principle (Australia Sydney)

- the fundamental counting principle (USA Florida k12)

- zero is not a number (Australia

- fundamental counting principal using tree diagram (USA, California)

Actually, this next figure is a diagram of a tree structure of counting. The root of the tree is at the most left position. Each branching of the tree is drawn the numeral base.

- diagrams of succession (Ottawa-Carleton District School Board, Canada)

- fundamental principles of counting using tree diagram (Philippines)

Actually it is a tree process. The root of the tree is the unity part from there are growing branches of growing quantities. The universe quantity is a tree. Each quantiy is at a step of the successive growing form where there is no void between successive quantities.

This seems simple as diagram. However, it is the most important base for logic of space. Note that Space is both the Container and the Content. This reality fact is of a unbounded fertility of reasons in knowledge.

Counting Principe
For kids there are usefull exercices to make acquaintance with how to name a quantity.
For example how to count apples beginning by kid C successively follow by B then by A. After counting they learn on how to read the quantity counted, reading from A and successively follow by B and next by C. Kids will naturally learn what is the basic order of the universal succession principle. For example this figure shows how to count 130 animals and how to read and name this 130 quantity. With a team of 10 kids, they will learn what is great numeral quantities until a limit of 110 and how to write them!

This above figure shows how a spatial element (AB) should be the direct function of the Quantities. Spatial elements are the direct FUNCTION of Quantity. Because a point and a line are Matter. As Quantity is concerning the Matter then a Space element is necessary the direct meaning of matter Quantity.

This is not a speculative discourse. The Dakhiometry had define all a system of SPATIAL REPRESENTATION OF QUANTITIES. And any calculation on space transformations is determined by a complete system. It can do better than the complicated Algebraic tricks and recipes for the fallacious pythagorean Numbers manipulations.

I am sory to thell that the current Mathematics is unhappily a true simplistic kid's invention where the Big container of Irrational Numbers is a Big one for Mathematics Ignorances. These are learning the consciousness of things and their precise defined quantities.

Mnemonic of Life Basic Logic

- elemental succession (, USA)

It is an exact expression.
The Succession is a concept that designates a concrete process of discrete or elemental matters. It is because only one element can be a succession of an another one. One element location should do one bounce to be in a next localisation. In the immutable universe there is the Conservation principle, that don't allows overlapping of matter. Space locations as matter is then the space of successions of locations. For example it is a contradiction for Continuum dogma to assert that one can count in the Continuum. Because the first continuum definition is that it is the No-Succession world.

In Dakhiometry knowledge starts on the fundamental life logic consisting of distinguishing Discrete Matter principles.

This next diagram allows to memorize the difference between matter Succession and its corollary, the Quantity.

Succession and Quantity

In (1), Succession is inter-object FORMLESS placements characterized by the Without-Limit.

In (2) its corollary,
According to the Succession Principle, forms in the universe ares possible. With forms, there are matter limits. Between limits of forms, are generated Quantities.

Limits of Succession create a Beginning and an End that characterize the Quantity. And Quantity is uniqueness according to the Matter Conservation Principle. These are basic Matter Facts that allows human Counting a basic necessarry Life technique for human and also for all the alive.

However the Counting remains so confusely in all the human though.

This diagram represents how to distinguishe and memorize it the difference à Succession Principle and its most important basic human capacity of COUNTING. We can see that the Quantities are limited by two ends. Usually, we use mixture of Quantities and Succession process. Thus, Quantities classed by succession of succession of quantities are really the Basic foundation of the Homothetic Figures. This definition is unknown until now.

On figure part (2), ZERO is clearly a Limit human language symbol. Zero is Not-a-Number because it is not a Quantity. The Anciants and Modern mathematicians have erronneous concept about ZERO because they don't have no conscience on Quantity Definition.
Thus ZERO means only a beginning and an end Limits for defining quantity.

The most mistake is to confuse Number with Quantity. Therfore, since the anciant time using number as mathematic elements (Arithmetic and Algebraic), the World is made by the human language laguage. That is to say: the World is CREATED by human with his imperfect knowledge.

- "laguage" + as + arbitrary ++ rational (Philippines)

- pi + and + imaginary + number + joke (USA)

How to spatial calculate the Space Constant?

- immutable law (Netherland, ING Bank)

- squaring + the + circle +++ "intuitibe" ++ mathematics (USA Illinois Chicago)

Space consciouness is necessarily intuitive because alive moving capacity need to have a global view on space. This capacity is actually the human intuition capacity.
Concerning the squaring the circle resolution, it is rather a precise result of a defined problem. From there, successive reasons are deduced in series. The layout of the squaring a circle problem is as follows:

Considering an imutable structure of circle inscribed in a square, what can we do to define precisely the difference between these two figure aeras?

Because this problem resolution is starting from a precise defined issue it can be tell that the process of deduction is then a reasonning development towards a some answer. Even if in the underground we rest always on the mode of intuitive though, the analytical reasonning is a fertile complement for a global thinking. If only an intuitive mode is a guide for problem resolution, a theorem can't never be proved but always verified.
In fact, it is in this way that the squaring a circle can be resolved. There is a basic proof of the Squaring a circle that rests on how and why we can measure the difference between the aeras of the circle-square in their common struture.
I did really a proof of the squaring a circle that is no more exposed in these texts. Origin of the squaring a circle is not due to some chance. The fact that from year millenaries the squaring a circle is never resolved, proves that there is no hazard in the universe.

The hasard is then necessarily defined as:

1) - A creation of events from Nothingness.
3) - An abitrarily choice between a given set of already prefefined existing events. In this case, from where comes from this set of these events? Finally, this means that all the universe events are from Nothingness.

Because in this case theses laws are not universal. No reason asserts that our Universal Laws are made from Nothingness. If we note that universal Law means "happening in the whole Ubiquity and also Immutability or No-Time".

- i + need + to + make ++ a + "cicrcle" + graph + on + the + computer + how ? (USA)

- if + square + is + you + triangle + is + us + cirle + is + ok + what + is + zero-logic (Japan)

- how + we + drive + value + of + pie (Pakistan)

- history of pi day (USA New York k12)

- history of pi (USA Georgia)

- how + to + make + a + teaching + device + in + the + value +of + pi (Philippines unep edu)

- pi de David Hilbert (Portugal)

- Squaring the circle (Indonesia)

- square the circle (UK)

- squaring the circle (Malaysia)

At first it is given there a third method to perform the squaring a circle.
This shows that the Dakhiometry Space Constant is really an immutable property of the universal circle-square structure.

- discover square wheels.gif (Lithuania)

- geometry square inscribed (USA mia)

- squaring the circle (USA Hawai)

- square a circle (USA msn)

- square and circle (China)

- how + do + u + determin + the + aera + and + perimerter + of + a + "squar" (Canada)

- mathamatic bearings (Papua New Guinea)

- détermination + de + Pi (China)

- inventorofpi (USA Florida)

- formula + for + squaring + the + circle (USA Florida)

- "cricle" and a tangent (USA Indiana k12)

- final + fantasy + The + Cristall + Bears (Cuba)

- Where + is + the + beging + of + a + circle (Canada)

Where is the beginning of a permanence?
Because it receives so many emails for a such problem the circle decided to transmute into the reality a tool denoted as a Square for the universe measurement possibility. It began to do like as follows:

The counting - space simultaneity (, UK)

This the basic consciousness of space property. Space is absolute. This is to tell that any point in space is immutably defined. This the simultanneity concept and it allows a fertile knowledge on matter space constructions..

- Squaring the circle (New York, Rochester Institute of Technology)

- c1 discontinuity (Japan)

- squaring + concrete + formula (USA Oregon)

Also, for any space scale, C1 represent the permanent relationship between a surface and its double. Particularly, C1 contains the define ratio between a circle surface to the square one circumscribed to it.

- Viet Nam geometry (Vietnam)

It consists here to produce a square (S) of aera equal to the circle (C).

After constructing and placing the little circle (C1) at the square center, two tangents of (C1) drawn from corner A and B of the square intersect themself at point (M).

The point (M) is the middle of the square (S) side. (M) is the middle of side EF of square (S).

- formula for squaring a foundation (USA Oregon)

- tangent of circle finite analysis (USA)

In fact, the tangent of circle (C1) is only a way for memory. The segment AM can be defined by the intersection of (C2) and (C) at point (M). The aera of (C2) is twice the (C1) one. See further figure for the circle aera definition.

How to use the spatial structure of a circle-square structure to spatial calculate the Space Constant of this following formula:

- proof + pi + raised + to + the + pi + rational (North Park University Chicago, USA)

- pi rational (, ottawa, Canada)

- Korea + pi + rational (USA MSN vzw)

- Greek + mathematician- + unresolved + value + of + Pi (Australia Victoria)

- greek + mathematician + calculator + of + unresolved + value + "if" + Pi (Australia Victoria)

Space-Cst= [(sqr(2.sqr(2)-1)+(sqr(2)-1)]2

- "alebraic" images showing relationship (South of Florida, USA)

This is a proof of algebraic imprecision...

- proof: an introduction to higher mathematics (USA wv)

- eureka rational (UK Virgin Media)

- higher mathematics formula (Latvia)

- MATH formula (Korea)

- maths formula (Australia, Victoria)

- Gods mathematical formula (New Zealand, Wellington, Palmerston North, Auckland Massey University)

- mathematic formulas (Japan, Kyoto)

- Maths formulas (UK, Leicester De Montfort University)

- calculation math (University of KwaZulu-Natal, South Africa)

This mode of calculation is done on the basic space element quantities. The Space Constnt calculation given here, is not a particular case of calculation. There is a method of determining any space dimension according to the four basic calculation operations as the addition, substraction, multiplication and the division. Obviously any algebraic calculation can be preformed by this spatial method. It represents the precise and exactness of quantity reality while the algebraic language convention tools are full of irrationallity unknown holes.

Spacial Calculation
This next figure-part-(a) show how construction of the space-constant give the value 3.12...
This value was determined as given by the above formula.
Now as a reciprocal calculation way, how can we do to construct this formula with space elements?

For this purpose, we start on the structure given at this figure-part-(b).
Note that modern computer can use CAD program that can culculate figure lengths. This way of calculating lengths rests on the internal program convention of a unit length for internal calculations. One can drawn from there any length equal to 1.

- 45 + degrees + circular + area (Cyprus)

You are right.
The quarter of a circle aera of S=k.D2 is equal to the aera of the circle of diameter (D/2). This latter aera is equal to the "Pi" value relatively to the scale of its spatial figure.
There are more many wealthy interesting relationships given by the Spatial Constant denoted here as (TT), when one use the Spatial Language. Particularly, on aeras delimited by an arc and segments, as for examples, the ones on this next figures.

Spacial Calculation

- circles with area pi
(Japan naruto-u)

All these cyan colored circles are of space constant aeras.

The Space Constant can be get from a circle of diameter 2. It can be written as:

TT = k.22;

or :

k = TT/4 = 0,78004843...

Therefore, what we tell from the squaring a circle is only a value proportional to a basic real constant denoted here by (k).

Therefore, the above figure-part-(b) can be choose as a basic structure for calculationg lengths of figures.

On this basis it is shown in the following how to construct the above formula.

However, because the current arithmetics standard is wellknown, the numerical value must be considered only as verification of qpace construction. Because the space construction gives necessarrily a Rationnal exact and precise lenght. That is to say spatial calculation never give irrationnal number.

The Dakhiometry can do complete calculations-by-construction for any scale of figure. The scale defined here is only for everybody more easy understading.

- pi drawn around a circle

There is a unique certainty about a length. It is the length of the Space Constant. We are certain that this Constant length is both the staight line and the curvilinear one! Wealthy consequences can be deduced from this base.


- square inscribed in a circle, find the area of the circle (USA California)

It is easy to see that the square where a circle is inscribed has an aera two time the one of the square inscribed in this circle.

To calculate the aera of a circle as function of its inscribed square, we will use what these two figures have as common length. It is the diameter D of the circle that is at the same time the diagonal of its inscribed square.

So, the aera S of the inscribed square is equal to the half of the one of the square where this corresponding circle is inscribed. We write as:

S = D2/2   or    2S = D2

We know that the circle aera C is:

C = (Pi/4). D2

Therefore it can be stated:

Theorem of the circle aera C as a function of the inscribed square one S.

        C = (Pi/2).S

- rational + pi (, Germany)

- pi + is + rational (USA Florida Tamu edu)

- pi+is+rational (UK)

- "mathamatic" + pi (Germany)

- is + pi + rational (USA Kansas)

- pi + is + known + to + be + rational (USA)

- pi + is + rational (USA)

- What + does + is + mean + to + square + a + circle (USA)

- pi history and the formula of pi (New Zealand)

- a circle that demonstrates where the actual measurement is derived for pi (USA Georgia)

- scientists + give + each + other + "hight" + pi (USA Virginia)

- did + proving + that + a + circle + can + be + squared + have + something + to + do + with + pi (USA Illinois k12)

I had exposed this problem all along my texts in this website here. It was exposed all the aspects and consequences of the squaring a circle. There was not only the quite particular aspect that an Old Pi is now seeing as a simple trick to approximate a factor denoted as Pi, to measure the circle circumference. Particularly, there is no ideologic discourse in may texts. And if there are ideologies, they are from the current world the ideology of them is to protect their stake and not according to human reason of science.

If there are someones that tempt to preserve the old erroneous Pi as constant for Mathematic caculations, it is no more concerning my responsibility.

The rational signification of the squaring a circle is the CERTAINTY of getting the Space Constant. This latter is the absolute knowledge key allowing the precise measurements of the universe space. The problem of squaring a circle is not a game and riddle for mathematicians entertainement. Because resolving the square transformation from a circle is not only for a quite exact and precise particular and specific old issue. This latter was done approximatly for a circle circumference as a function of its diameter according to the Old Pi. The Space Constant is a more general wealthy reason conquest to get into the forms of space that human necessarry need for their technology.

Thus the squaring a circle is a general useful and indispensable key for a human advanced knowledge. Because of it general quality, the Space Constant is also the solution for the usual particular problem concerning the circle the property of that was NEVER really known. For example, amongst many possibilities, the Space Constant allows to know what is precisely the circumference and the aera of an ellipse while an old Pi can't give any idea on this issue.

The response to this question is:
The solution of squaring a circle, is the one to resolve precisely and exactly the circle circumference. It allows to get the Space Constant, the absolute solution that an old Pi can never assert.

- how + many + points + of + pi + are + in + the + circonference + of + the + universe (USA Georgia k12)

This is a fascinating conjecture.
May be one of your searcher or any other one on Earth will have some answer one day. In this time, the universe space will open to human. trips.

- inventer + of + pi + 3.12 (USA)

This day on March 2008 is now really the "Pi Day". Because it is the First Time that someone tells practicaly the numeral 3.12. Good! It remains for the billion of little calculators on Earth to tell simply the same truth. What a world more infinite than the universe!

- set + induction + for + circle-mathematics (Malaysia)

- great world "matematic"

- pie (matematics) (USA Viginia k12)

- PI + in + "matematics" (Kyrgyzstan)

- real + value + of + pi (USA Wisconsin)

- mathematic (Poland)

- - why + do + so + many + modern + round + objects + not + equal + pi + when + the + circumference + is + divided + by + the + diameter

- mathamatical instruments (Sri Lanka)

- "MATEMATICS" limit (Turkey)

- End + segment + method + of + computation + of + pi (USA) - higher mathematics (USA Miami)

Calculation layout

- proove + Pie + is + 3.14 (South Arabia)

Actually, here in the following, is the proof by spatial calculation, how Pie is equal idirectly to 3.14.

- purebasic + pi + calculation (Thailand)

- what the impossibility theorem really is (USA New Jersey)

- what + us + value + of + pi (USA Texas)

- Geometric Solutions of Algebraic Equations (Korea)

- greek + scientist + considered + to + be + the + greatest + mathematician + of + the + ancient + world + who + calculated + the + the + unresolved + value + of + Pi (Australia)

It was Archimedes. But how he did exactly these calculations is really unknown.

- value + of + pi (USA, Colorado, Boulder University of Colorado)

- formula pi (Portugal)

- pi compas (Mexico)

- pi + value (Ukraine)

- calculus gif animation (Lebanon)

- Algebra off course (Peru, Carvajal Co hace las cosas bien)

... of course, really. It can be constructed (calculated) any length of the space structures more than Algebraic methods can do and imagine. It is to say the one real human knowledge should be to get back and to regain his basic capacity of linking to rational space, the reality needed for the life development.

- pi geometry (Croatia)

- Pi + 3.12 + Indiana (USA, Ohio Cleveland CaseWesternReserv Univ., student cwru edu)

- how + accurate + is + Archimedes + value + of + pie + compared + to + the + values + known + then + to + the + values + know + now (optusnet, Victoria, Australia)

Fist pioneers!

- pi + accurate (Vietnam, Viettel)

- Mathamatics + new + invention (

- Greek + scientist + unresolved + value + of + pi (, Melbourne, Australia)

- new pi formulas never used before (, Alabama, USA).

....... while our current running date is 2011.

Let us construct the corresponding value of this equality:

Space Constant

Here denoted as:

Space-Cst= [(sqr(2.sqr(2)-1)+(sqr(2)-1)]2

Spatial calculus of this equality is done progressiveley as follow:

R1 = (2.sqr(2)-1)
R2 = sqr(R1)
R3 = (sqr(2)-1)
R4 = R2+R3
Space-Constant = [R4]2

- how + the + children + reads + writes + and + understanding + in + class + at + biginning (, India)


All of existing languages are language for reporting realities. Thus, human language is only memories of realities. It is only formed with realities consequences. However, these latter are not always fully accessed. Human language are thus necessarry the product of anthropomorphic realities. Human languages are then consequences of imperfect reality notions. Therefore, no language can be creator of reality.
In the other side if human has the property of knowledge on himself and on what are realities surrounded him, this means that there is a direct link between oneself with what is not oneself. There is a direct link between oneself with the whole reality. This link is denoted as the unique universal language, the one of reality consciousness. For example, measuring precisely something is a direct link for accessing to a reality. Reality is no more than the World presence.
we can tell that this direct consciousness of reality is the Mathematics Language. However, the true mathematics language is only concerned on direct reality consciousness and not what is usually known as mathematics formalisms. The true Language is the consciousness of the fact of space matter structure. Reality is founded on these universal structures from where changes of reality forms are constructed. It is why knowledge on this direct universal reality language allows the understanding of natural phenomena and also allows the possibilities of human action for reality constructions.

- circle achitecture (Korea)

Actually, space is architectured and architecture is space.

- matter + universe + is + constant (Canada)

It is why any form transformation is perfectly and precisely defined by law of logics.

- PI ACCURATE VALUE (, QuinetiQ, Inspired solutions for a changing world, UK)

- most + accurate + value + of + pie (Singapore)

- natural + formula (China)

- pie proof math (Thailand)

- rational + form + of + pi (USA Berkeley edu)

- calculationg true lengths (UK Grimsby)

- "mathamatic" + signs (Canada)

- square root (Greece)

- geometry plane line intersection (Romania)

- one circular object with progressive rhythm (India)

- instruments matemátics compas (Spain)

- spider circle square (USA) - how + to + proof + equation + circle (Qatar)

- define full circle (USA Arizona)

- mathematics and circle pi (Georgia)

- The + ultimate + value + of + PI (Ireland)

- PI + accurate (South Africa, University of Cape Town, Wamkelekile Iunivesithi Yasekapa)

Spacial Calculation

Let us construct at first
R1 = (2.sqr(2)-1)

According to the above reference figure-part-(b), we get a circle of radius equal to R1.

- step by step procedure to approximate value of pi using only a perfectly straight stick (, Oklahoma, USA)

- how to determine space needs (USA amer-Honda)

- square root of line (, New York, USA)

- big circle dia measure (Korea)

- not wear a mask (Indonesia,

In second, il will be determined the square root of
R1 = (2.sqr(2)-1)
That is how to determine R2=sqr(R1).

Spacial Calculation

A circle of diameter AB=R1 is drawn. This latter intersects the unit line at point (H). We get then:

Segment AH = R2 = sqr(R1)

Next it will be to construct the length
R3 = (sqr(2)-1)

- how to construct a prayer wheel (, Hertfordshire University, UK)

- how to construct a wheel giant (, Portugal)

... for a great funfair?

- construct a Tibetan prayer wheel (Singapore)

Many more prayer wheels for a better world.

- Srilankan students Hertfordshire University

- Hertfordshire university (China,

- Tibetan cosmology (Brazil)

- Tibetan prayer wheels (, USA)

Spacial Calculation

This is to construct length (sqr(2)) subs length=1.

This is given directly in the above referent figure. We represent R3 as the radius of a circle as is shown on this next figure.

Spacial Calculation

We can now construct the following result as:
R4 = R2+R3

This construction is straight direct. Thus, R4 is obtained.

The construction of (R)2 is given in the next following shematic.

- can be calculated by using the following formula (Russian Federation)

Any quantity of the space can be PRECISELY détermined by construction.
The numeric system was only a conventional subtitute for defining a quantity when spatial construction is ignnored. Quantity is necessary the total discrete Points of Lines and Curves. Note that a given spatial construction is universally determined when defining any given Figure unit. It can be perform all the usual types of operations used un algebraic and arithmetic numeric methods.

- Practically proof of value of pi with figure (, Nepal) - excat + value + of + pi (Nepal)
Pi Length

Here is how to get the (R4)2

- gif construct a circle and show how to find pi (, Oregon, USA)

Pi Length = AP = (R4)2

- The + Law + of + Conservation + of + Matter + animation (Virginia Institute of Marine Science, USA)

Actually. Space is a matter. No need to any approximation method, the Squaring a circle is possible as concept and as transformation only according to the precise matter law of conservation.

- a pi + squared + proof (Canada)

- easy pi explanation and calculation (, Australia)

- product structure calculation how solve (Singapore,

- the + accurate + value + of + pi (Singapore)

- most + accurate + compass + and + easyest + to + use (, Moutain Telephon, Kentucky, USA)

- enters an accurate value of pi (Phenix, USA)

The only absolute precise value of Pi is only given by a length. For example, on this figure Pi is the segment AP. It happens when an unity length is defined for this figure drawing. Or if there is no particular defined unity then, the length (AP) can be taken as the constant unit of this drawing. This a great practical advantage of spatial construction method. It is why the Dakhiometry denote this Length as a Spatial Constant et not only some the usual means for circle diameter measurement.

Numérical value given by any calculator, suffer errors due to numerical conventions on defining quantity as Number with language alphabets.
Only spatial construction can define precisely any length. There is really spatial constructions that can do any complex calculations according to the four basic operations to define any absolute precise quantity. It is done in their continuity of quantities without a lack in this latter. - formulas + de + pi (Columbia)

Spacial Calculation

Finally, how to do R4 squared?

For this purpose, the circle of radius=R4 intersects the vertical unit line at point (T).

Now it can be drawn a circle of diameter AP that also has a chord AT.

Final result:

AP is the result of spatial calculation for the formula:

AP= Space-Cst= [(sqr(2.sqr(2)-1)+(sqr(2)-1)]2


The Space Constant is concerning all the universe space, WHEN A GIVEN UNIT IS CHOOSEN

For example when the Space Constant Length by itself is chosen as this Unit.

fundamental of Science Accuracy:


In spatial Language,
whatever is the choosen UNIT-Length:


The space structure of this above next figure and also the Pi-Formula prove directly this


Suggestion for scientific definitions of Basic Measurement Quantities:

The Absolute Space is a basic factor for a best understanding on the universe transformation phenomena. Until now the Metric system was invented for science accessing to phenomena. However the Metric system is only a relative conventional one for human use only. There are many types of reference for measurements in the world.
Now, it is an advantage to rest on a true unique universal reference of quantity measurement.

Therefore, it is more general to define a universal unit of length getting directly from universe principle according to the Absolute Space where a rational Universal Space-Constant of length is precisely defined.

The so mystic Pi of 3.14116... on that man was suffering so much difficulties:

a) - At first, it is as a Ghost indefined quantity.
b) - And then, Pi is only some mystic irrational Number from also an artificial Magic Number denoted as universe Archetypal, the one from an undefined Nothingness of the universe.
c) - Finally, this Pi was mathematically sa colled proved as the FACT of Impossibility Part of the Univers...

Now, the Universe Space is proved as being Absolute. Thus, true human Science should rest on true rational defined of accurate unit of Length.

Drawing a geometric figure need at first to define a unit Length.
The figure unit needs only to choose any-given-Length.

A universal measurement reference is a great benefit for modern anti-wasting industry activities on Earth.

Modern science should work for defining a new Universal Measurement of Forms in the Rational Absolute Space of the Universe. The new discovery of the Length Space-Constant, should be the Root for establishing a such New True and Real universal practical system. Why does The-SPACE-Constant can't be the the Universal Unit of length???

This is for Man the main necessity.

The fortune is smiling on human. The wealthy construction is the property of the universe. E.T. peoples is surely a facts in the universe space. The probabiity of an alive planet like the Earth is low. More, the discovery of the Absolute property in somewhere of the Space for an E.T. finding a physical Space-Constant may be very rare.
Therefore, when Man was really hitting by the stroke of luck in finding the Absolute property of the Universe Whole Space. The Universe will be assuredly the place for New Man's Earth-Sciences with the new potential capability for his space exploration. The vast whole Universe Space during the next Futur will be his interested field.

May be, we have to expect:
Man get there a new chance and a new key on the universe knowledge.

This is the sign of Man fortune, to be a futur
I.T. for somebody, elsewhere far from the Earth and somewhere in the Universe vast Space!!!

Example when the [Unit of Figures is defined by
The Space-Constant as the Figure-Unit]

Here next, is concerning a Dakhiometry-Conjecture Concerning the universe Absolute Space:

What is the meaning of the Space-Constant?

(From Length = Number (1)
into [Space-Constant Length = as Unit].

The result is that we get:

A figure of Cercle Unit with :

Diameter = Unit

And a Cercle Unit with aera = 0.25

It can be seen that the current Man's traditional Mysticism of Circle is vanishing for ever.

For the Straight Length,
the Metric may be also progressively changed into the universal Space-Constant Unit.
But there, man will meat his Traditinal Inertia contradiction...

Do you have some understanding about the Absolute Space, after somme millenaries living under Nothingness and Relativity believes???


From millenary, Mathematics was searching the Pi value particularly the Pi-Length.

However, what is this so-called Mathematics Length of Pi.

And now,
What is the meaning of the Absolute Space represented precisely by the Space-Constant???

The fundamental Space Constant length is strictly rational

- square root of 2 is rational proof Philippine university (USA)

- Tangen Politechnic Norway (Poland)

- most + accurate + value + of + pi + ever + generated (Philippines)

- equivalent diameter circle to square (, Virginia, USA)

- prove + point + p + to + line + l + is + unique (, California, USA)

- how + will + you + use + the + circle + to + prove + the + value + of + pie (India)

The Space Constant Length is a Rational quantity.
A) - Because its length is constructible.
B) - Because it proves that the circle and the square perimeter are exactly equal. This is proved in the following of:

The squaring a circle according to equality criterion

Squaring the circle perimeter

This next figure shows how to square a circle with the criterion that their perimeters are equal.

This construction is possible only as down-stream consequence of the squaring a circle with equality aeras criterion.

This can be done according to the following logic:

a) - We know how to construc the initial squaring a circle of diameter (D = MN) using the little circle (C1).

From there it is deduced the Length:

AB = Pi

In such structure, this gives the formula of any circle perimeter as:

Perimcircle = Pi.MN

From this base, it can be induced that in any of this structure, a square (ABCD) perimeter is:

Perimsquare = AB.4


Perimcircle = Perimsquare

Pi.MN = AB.4

Finally, when the old Pi is renamed as Space-Constant then,
The Space Constant, is given universally in any of this circle/square structure, by:

Pi = (AB.4)/MN

This logically means that in this structure, the square perimeter (ABCD) is always equal to the circle one, as 4 times the symbolic Pi length (AB) of any figure scale.

Such equality comes from the reason that the quantity (4), is no more than the SCALING FACTOR for the Pi, in any figure scale.

It is why
in Dakhiometry the old name Pi, is more Justly denoted as the Space Constant provided that it value is always valid in any space scale.

Fantastic isn't?!!!


Theorem of the squaring a circle on the criterion of perimeter equality:

According to figures by spatial construction, with perimeter equality criterion, the squaring of any circle of diameter MN, whatever is its dimension scale, the perimeter of the resulting square is always equal to 4 times the Length AB.

This next figure resumes the squaring a circle of diameter MN with:

1) - In red color, the square under aeras equality criterion.
2) - The square ABCD is the result of squaring the circle, under perimeters equality criterion.

Consequently, this means that:
The Space Constant Length AB is a RATIONAL QUANTITY.

In summary
The universe Absolute Space is characterized to have the two properties of being Curvilinear and Linear.
The Absolute Space is then defined by ONE Constants in the two forms concerning the Quadratic and the Linear ones. They are given through the Circle to the Square Transformations
The unique Space Constant construction is given in its two forms on the above figure and next under two numeral form representations:

Absolute Space Constants

Under such spatial forms, the direct and the reciprocal of circle versus square, can be get easily when is given AB or MN.

Written under the old rigid Number form is:

Absolute Space Constants

- the + numberto + of +pi (, California, USA)

- did Archimedes use area or circumference to calculate pi (UK)

It is to don't-forget-me.
In anciant time Euclide try to see the factor that link between a circle and a line. This comes from the fact that a running wheel performs a rotation cycle with its diameter. It is the same problem that Archimedes temps to resolve. It is to resolve the circle circumference with equivalent polygons.
Thus the classical Squaring a Circle is concerned only to know the circle diameter as a factor given by a circumference Length. Extended to the aeras equality is due only to that it was supposed that the diameter of a circle is probably concerned as a common factor.
But really, Aeras or Circumferences are not clearly defined as a "to be or not to be" way for resolving the squaring a circle.
Thus logically, it should be stated that:
When one had done the squaring a circle, one should underline this common factor as both the Aeras and the Lines as this equalities or this unity in the circle-square equivalence.
Consequently, this unity has the main meaning of the Universal Transformation Constancy, the property of that defines the concretness of the Absolute Space

- how + do + you + know + that + squaring + is + a + reversible + operations (, USA)

- The + mathematical + nature + of + PAI + forbids + the + construction + of + a + straight + section + with + a + length + equal + to + the + perimeter + of + a + circle + using + only + ruler + and + compass. + as + well + as + the + squaring + of + the + circle (sbcglobal.netn USA)

May be, "PAI" is the problem key.
Because as shown in the following, it can be easily constructed the length of the square (K2) perimeter equal precisely to the circle (Cs) one.

- equivalent diameter circle to square (, Virginia, USA)

- the application example of regions between circle and square (, USA)

Actually, comparing circle to square and consequently to any other form, is equivalent to compare precisely, square to square or circle to circle.
this can be done universally whatever are concerned any scale in space.

- animasi + mathematic + chapter + circle (Malaysia)

- walking along a circle with rational step (, USA)

- Discretness + of + a + scientific + text (Ukraine)

- equivalent square for circle (Madison, Wisconsin, USA)

It is really what is the rationnal fulness in EQUIVALENCE as relationships meaning. The euclidean Equality by Superposition is only a particular empirical statement.

- mathematical impossibilities (Australia)

- a circle is inscribed in a square. Remove the corners and the perimeter stays the same (USA)

... the perimeter of this cercle and this square with its new aera.
Actually, it is because this new square is in fact, the result of this circle squaring. Really, the squaring a circle has the simultaneity property for the universe Beginning event where process of construction was starting at a whole. It is the characteristic of the whole universe Absolute Space. This explain the pertinency of the Dakhion ubiquity as a physical property.

- Determination + of + the + value + of + pi + theory (Ghana)

- which + mathematician + founded + a + society + whose + logo + is + a + "sqared + sqare" (India)

It can be noted that the squaring a square is neither forbidden nor impossible. One can do easily the squaring a square, with a circle as a relational medium.

- ETBU + immutability (USA)

- universal + factor ++ mathematics (Niger)

It is the TRUE Space Constant. Consequence is that Locations anywhere in tbe universe space structure, are perfectly and immutably determined in their forms. It is why any form and quantities, near by or far aways from an observer, is always in its same form and quantities. The perspective view is only an illusion factor in three dimension that is only significant as 3D scales.

- Principles + of + Consequences (Austin, USA)

- New Pi Theory (Croatia (Hrvatska))

- circle + internal + square (Ireland)

Actually. Pregnant Circle.

- THE + CIRCLE + AND + PI + AS + SYMBOL + OF + INFINITE + LIVING + MIND (, South Africa)

- elements + of + construction + law + in + Malaysia (Malaysia)

- squaring of the circle problem proof (, Pennsylvania, USA)

- space + structure (Vietnam)

- equivalent circle AND square (, Canada)

- Transmutation circle (Ukraine)

- using angle properties in Circle art (Manitoba, Canada)

- transcendentaal pi (Netherland)

- equivalent + square + from + circle (, Canada)

This is a just expression on this problem. It is because equivalence concerns any physical factors that can define objects.
But when was tell as the Squaring a Circle, one shows that this problem concerns to adjust different Forms, like what a blacksmith was working on iron material. Mathematics are mainly as mechanical manipulations. It was this method that Archimedes had used in tempting tp resolve his Pi and his Method. They are only mechanical manipulations. It is because
the Geometry was and is to day, the erroneous idea resting on MORPHING things.

The Absolute Space is multiple in its differents in its uniqueness and multiple of structures. But Space is not contradictory with the possibility of Morphing Space as it is basically stated by the Relativities theories. Therefore, the Reltivities stay in the inheritance of the old millenary belief of the Geometry Morphing method.

- pi is rational (tamu.deu, Texas, USA)

- Which is an accurate description of pie (, USA)

- Intrinsic circles (, Buffalo, USA)

Really, the circle is intrinsic to any linear figure. The circle is trully the root origin of Forms in the universe. Forms in the universe is as the Tree, where the root is the Cricle Circle properties. It is why the Space is both Isotropic and Homogeneous. At the origin, the Space is in Permanent state. At this time tne universe is circular and the spase is only Isotropic. When appeared the Linear property in space, this latter get the property on being in the capacity of matter in mutual interaction. The universe Beginning can then started according to the event of the Squaring the Circle process for the fulness of Isotropic and Homogeneous Space properties.

- fullmetal alchemist transformation circle (USA)

- taoist + squaring + the + circle (k12, Ohio, USA)

- Constructing + The + Universe (Vietnam)

- demonstration of squaring the circle (Bolivia)

- squaring + a + circle + is + possible (Brazil)

- value of pi IN UNIVERSE (, India)

Actually. This value is a Universal Constant as due to the construction by transformation property inscribed in the Circle structure. This universal property drives to great consequences. For example without this Constant, science will never kow matter Aeras and Volumes than only acoording to the empirical methods. Also, the existence if a such universal Constant, shows that the Relativity theories are quite born from a huge fantasy.

- geometrische + konstruktion + von + harmonischem + mittel (Germany)

- new pi circle (, Texas, USA)

- all + truth + can + be + circumscribed + into + one + great + whole (, InsightBroadband)

We can actually determine all the principles from there are originated all the Truth as a Whole that we human can access. All the truth from there are formed our rational knowledge.

- new + pi + value (, BlackBerry, USA)

Next figure resumes a more deeper inside view of the Squaring a Circle properties.
Absolute Space Constants

In fact, there are really a double equivalent results given by the squaring problem solutions. The Key (AB) of this problem gives rise to two solutions of transmuting a Circle into a square in both Forms of equalities as follows:

1) - Transformation under Equality of Aeras.
2) - Transformation under Equality of Perimeters.

It show that the ratios between the three Circles and the three Squares circumscibed to theses circles are equal to the same Space Constancy divided by 4.

The consequence are also to give the different angles characteristic to these transmutations. These angles are the right angle of a square. Therefore, we can tell that the squaring a Circle gives wholy the 3 characteristics of a square as:

A) - A Length.
B) - An Aera.
C) - And a Right-Angle.

Fantastic isn't?
In fact, the Circle produces a turnkeySquare or a ready-made Square for the Beginning of the universe construction.

A such universal Constancy in the universe space misrepresents the Einstein's Relativity where his mass-spatio-time can be deformed at any time and where the Space can have no determined form.



This above equality is spatially constructible.

- precision measurement through the verification of pi (, Philippines)

- true + value + of + pi (, Switzerland)

- how + accurate + is + pi (, USA)

- how + are + the + digits + of + pi + calculated + and + when + calculation + how + do + they + calculate + it (, South Africa)

The denoted quantity problem is not resolved until now by any existing science.
Because until now quantity is only a language word know as conventional Number. A word Number is significant for limited particular quantities only by convention. Quantities obey to the universe principle of discrete Succession continuity. Thus whatever are word that language can invented, they are only imperfect image of the succession. For example the decimal Number can't represent the true successive quantity of matter. The Number words as base to represent quantities are necessarily a distorsion of the true quantities. Mathematics had invented the Irrationallity and the Real Numbers. These methods are only mirages of quantities continuity. Now the modern digital technology is only the direct application of thes Numbers mirages. As for the Achimedes' exhaustion principle, any digital calculation, as wide as their digital words length are, is necessarily like the Achiles running after the Tortoise.

The current Sciences don't know how to dénote any precise quantity because of their belief on the Number illusions.
Only precise quantities can be in concret terms represented by space elements as point and lines. This should be a futur issue that science have to resolved. In the meantime, any quantity represented by the language words as Numbers, is only approximation that can't goes further than a maximum of 4 or 5 decimals. Practically quantitiy precision remains the same known and established by Euclide that are no more than some percents. For example, the formalism of [ 135 ] is only a mirage even if modern sciences rest on such convention. Error done with such formalism during long algebraic calculations where the Euclidean division algorithm is an another systematic source to complete for a total blurring of precision possibility.
So the so called infnite irrational value for the Archimede Pi is not a scientific problem. It is no more than a scientist pleasant applied mathematic joke like the Zeno's Aciles and the Tortoise. Really, there are too much basic things that the current sciences have to build to be abble to cancel too much of their millenary illusions.

- new + value + for + pi (, The University of Edinburgh, Scotland, UK)

- true + "balue" + of + pi + not + 3.1415 (, USA)

- line + circle + purebasic + intersection (Germany)

- pi + length (Hungary)

- the + square + root + of + pi (USA s.o. California)

On this above figure, AT is the square root of Pi.

- pi + rational (Germany Bosch)

- Physic + Scientiest + and + Mathematician + Formula (Malaysia)

Current science is looking the world through Relativity Optic

- how + many + centimeters + squared + equals + a + meter + squared (, USA)

Proceeding in such manner we get always:
(x centimeters)n = 1

That is to tell, human is always living in Relativity realm. He can know the world only by relativity in measurement. It is why human science needs so many unit systems for measurement.
Therefore, science can define something only in one choosen unit sytem. Thus, we can not measure something through two different units as centimeter together with meter. What we can do is to mesure things only with meter or only in centimeter. For example the good manner is:
(0.0x meter)2 = (y meter)2
It is the possible definition Relatively to the Meter as Unit.

Would our destiney be only in relativity manner?
The answer is no!
There is the unique good manner for science of measurement. It is the use of elements of spacial realm for science.
Because we can always measure or calculate a length (A) as the square of an another length (B) squared. The result is always unique in spatial language.
For we human, to read such results we need only to introduce in this system, a given length defined as the Unit of these measurements.
Finally, the only thing to do is to scale any length according to this given unit!

All these calculations rest on logics justified by perfect reasons that are not exposed here but can be verified by everyone everywhere in the world.

- religion pure geometry distribution (Australia, Melbourne RMIT University)

- advance calculation (, Netherlands)
Because there is really a complete process of spatial method for calculations with the four basic operations. For example, any point of rectangular aera can be precisely deternined by spatial calculation of multiplication or division this include root of quantities. This way of calculation is until now ignored because human was from millenary formated to the Arithmetics and Algebraic manner of seeing the world.

- miracle geometry

If this remark concerns the spatial calculation then it is really a most astonishing event for the usual one's habit of calculations. But considering that calculations are no other think than the space as absolute property. Absolute state means that everything can be defined and therefore, known from any where of space location. Precise calculations is the consequences of such space property. Manipulating space element don't know any hole necause space is the fullness of the universe.

- pi + value (Romania Craiova)

- circle squared geometry (, Ireland)

This next figure resumes all the above spatial constructions. It is here no more any resolution of old Pi using the impotent Geometry.

- geometry in circle square (, MLL Micro Leads Limited, Bangladesh)

- how + to + make + the + easyest + cake + on + earth + without + wipped + cream (, ACANAC INC Feature Panel, Canada)

- squaring method for building (, Trinidad And Tobago)

- Acanac logo (, Acanc Inc., Canada)

- background + of + the + pi + value (Kampuchea, Cambodia)

- National Academy for the Performing Arts-Trinidad&Tobago (Israel)

- method of gold secant (, Ukraine)

- achitecture in Cambodia (Cambodia)

Nice Khmer architecture art...

- Achitecture in Cambodia (Cambodia) - Cambodia architech (Vietnam)

- Khmer art symbols (, USA)

- building Cambodia new Khmer architecture (Cambodia)

Khmers are high artistic and inventive people.

- Cambodia architecture (Philippines)

- viettel post o Campuchia (Vietnam,

- Cambodian architecture diagram (, Washington, USA)

- modern Khmer architecture (, Illinois, USA)

- Cambodia animation (Malaysia,

- Arts architecture of Khmer (Cambodia)

- modern architecture in CAMBODIA (, Cambodia)

- what + is + the + most + acurate + way + to + express + pi (, NHS Your Health)

- student + is + attitude + toward + "mathamatic" (Thailand)

- pi + et + force + centrale (, Japan)

It doesn't appear obviously but this problem is the basic point root proving that until now, science ignore wholy the fundamental circular property of the universe space.

An universal Central Force is the negation of the concrete discrete space. A center is not a center if it is not defined. This point center is then obly the point where the Hasard will occur anywhere. This is no more than the universe depending to the Nothingness or Infinity. Nothingness is only a concept of No-Space. Paradoxically current science for example the Dynamics, where it rests on the universe described as Movement. It is because movements are the reality of concrete space distances. And really Movement as the Newton's Force, is no more than undefined. The Dynamics is then the attempt to describe the Relativity where nothing exist without being refered to some other thing, that in turn is no more defined because of their relativity. This is only the eternal existence of the hazardeous central force that finally was supported in its extremum bad effect, by the Einstein theory.

The Pi is no more than a exercice joke to get one unknown circular relationship in space.
But with the Space Constant, it should be disavow such current false science concepts.

- Calculating + Spatial + Resolution (..)

There are to much reasons to expose if the Dakhiometry Spatial Language have to be exposed.
However, it is the main tool appropriate tool for the universe Science.

Considering that the Spatial Language is direct manipulation of the universe real Space because this tool is no more than accessing directly the universe Space according to an homothetic sample of this Space.

It is not the case for the old Geometry. This latter is only a cobventional drawing that of figures replacing the words of a given talking language. That is to tell the Geometry may more efficient if one replaces it by cartoons or diagrams. Geometry is only a conventional incomplete language as like for the different Number systems. There, the symbols are only conventions. Like the modern numeric systems, that is no more than conventional technique for defining words that may carry any conventional meaning.

With the Spatial Language the difference is that this latter allows to directly work on the universe Space by using it on direct homothetic samples. The universe Space has precise basic alphabets when are used allows the direct understanding of the universe phenomena.

It is why the Dakhiometry Spatial Langauge can transforms the real Space for its constructions as the nature can do it. For matter transformations, it can perforem the addition, Substarction, the Multiplication and the Division by using directly the Points, Lines and Curves for defining Aeras and Volumes of any Forms.

The squaring-Circle can be completly resolve according to the Spatial Language. There is more definitions about the Squaring-Circle that is not exposed in texts of this this web site.

One can not clamed that hi is inventing the Suaring the Circle and consequently the Pi Value, if he dont know completly the Spatial Language... because the Squaring a Circle is directly the consequences of the Spatial Language Definition. There are more interesting consequences about the Squaring-Circle that are not yet exposed here. Particularly the squaring-a-Circle directly from pure circle elements.

This is to tell that without the Circular kknowledge there is no possible some ideas on the transformation of Circle into a square.
The fundamental truth is that with the current Mathematics the Squaring a Circle is really Impossible

It not due to mathematicians lack of imagination.
It is fundamentally due to the Mathematics ignorance on circular property ! The Circle is not simply from the machanical Compass.

Spatial Calculation

In fact, it is one of many method to resolve the squaring a circle (C) done in Dakhiometry. The purpose is to construct the Space Constant length AP from reasons found in the circle-square structure. The square transformed from (C) has AM as side.

- modern geometry constuctions (, Greece)

There is no spatial construction limit according to that space is structured and in any situation an universal structure can be precisley determined as reference of construction. And more, the four basic transformation operations is also properties of space. Therefore, with a more better acquaintance with the space properties human science can understand more easily natural phenomena and also construct his projects according to precise universal laws. This a reality fact and not an another modern ideology.

- rational + value + of + pi (Qatar)

- "Mathamatic" + concept + of + zero
- "Mathamatic" concept of numbers (India)

- what + happens + when + I + take + the + length + times + width + and + the + "suqare" + root (USA)
You throw away the root, find length=width and finally get a square as remainder.

We had gotten this formula according to spatial analysis of the Spatial Constant, given by the squaring a circle.
What is done there:
We was doing there the reciprocal of this formula according to the same spatial method.
It consists to find from a square, the basic remanences of circle from where a square is structured: the Space Constant. Because in a square, there is no known data to determine this Constant (3.12...) while only the circle properties allow to get it. In brief, a square can be transformed into a circle only and only, when a squaring a circle is yet known.

This is why until now, no mathematician succeeded to resolve the squaring a circle. All had trying to do the sqarring a circle, in tempting to make a ligne look like to a curvilinear one! That is to say: everyone had tempting to do the circling a square without knowing the squaring a circle.

You have gotten there the Mystery on the IMPOSSIBILITY of a squaring a circle!

The above Space Constant formula is really a spatial formula. It is a new aspect given by the Dakhiometry never known until now and obviuosly, is not a conventional Algebraic formula.

- "perfact" circle (USA)

All the numerical values that we meet along the squaring a circle are only used because of the standard habit of Algebraic an Arithmetics only known by the current Mathematics.

But really, it is shown here that calculation by spatial construction is the full rationnality of any universe quantity. This rests on a matter space fully defined as dicrete and absolute in location.

- can i get yo number (USA)

- square root (Canada)

- complicated math (USA)

- X-radius diffraction introduction geometry reciprocal space image (USA)

Reciprocal space is used as description for Crystal Lattice network in X-radius measurements.

- extraterrestrial + "prrof"

- why+pi+is+rational

- pi+is+rational

- exact+rational+value+of+pi

- most+accurate+values+ for+ pi+ calculation

- "mathamatic" + problems + for + find + out + ratios (USA)

- triangle unit circle (USA)

If we can construct an unit circle of radius=1, then any inscribed triangle must necessarry of decimal dimension below 1.
In Dakhiométry it can be calculated figure also of any scale known as decimal measurements. It is why there is no possibility of irrationnal dimension because space element is located always by a precise point. Therefore, if there was mathematics irrationallity it is due to the Numbers. These latter are created by human language that can't have the hyper high spatial resolution as for the universe discrete matter.

The true basic proof of circle Aera

The circle aera proof can be done only when a Space Constant is known. This latter allows to do the squaring a circle. Next, with the Space Constant the squaring a circle can appear. This step is the event of the possible measurement conscience for knowledge of the universe. Finally, according to the measurement possibility of a Space Constant as reference, the circle aera can be now formulated.

- Origin + of + the + value + of + PI Greek + word + for + circumfrence (India rbn gov)

- natural circle with diameters (USA Kansas)

- Pi + the + whole + calculation (USA so California)

- Squaring the circle, why (SouthAfrica)

- spatial structure (China)

- circle "area" equations (Canada)

- simple + proof + circle (, Germany)

- images with circle and rectangles (York University, Toronto, Ontario, Canada)

- basic design composition with circle and "regtengle" and "squers" (Jordan)

- spatial structures (, Russian Federation,

- most + exact + value + of + pi (Singapore)

One of the first practical application with such precise value, is to inroduce it in technology. At first, it is to have an international agreement to define a circle with this new value, for example include it in any mathprocessor and in digital processes programs as for any C.A.D used for technology conception.
This is a vast challange as industrial job to correct the current mathematic defaults.
Without this necessary task, any Mathematics enhancement will not be really useful. There are actually a huge amount of enhancements.

How to calculate the circle aera?
Well, for the new year 2008, it is time for all human on the Planet to use the most logic simplicity of spatial language to prove the circle aera formula.

Considering this next figure and with the Lamca theorem giving the equivalent rectangles from a square, the circle aera is directly given in the circle-square spatial structure.

Spatial circle calculations

On this next figure, we have:

the aera (S) of the square is
S = AM2

According to the Lamca theorem, this square aera (S) is equal to the rectangle one of sides AP and AD.

- cicrcle + with + pi + in + the + middle (, Australia)

- Robot vision equivalent rectangle (Taiwan)

It is a practical means for robot image processing precise calculation.

- rational root theorem (USA)


S = AM2 = AP.AD

This formula given by the Lamca theorem, is proving that a chord AM squared in the circle (C) is equal to the product of segments on its diameter AD=2R, divided by the height MP from summit M. (R) is the circle (C) radius.

According to the squaring a circle, the square aera is equal to the circle (C) one.

circle (C) Aera = AP.AD

- "cirle" "area" (United Arab Emirates)

- applied mathematics formulas (area) (Bloomsburg Univ. of Pennsylvania, USA)

- what is the formula for a solid circle (Time Warner telecom, USA)

You are quite true. Any spatial form is fundamentally solid objects. It is because space locations are basically discrete matter that we can have conscience and can measure any real thing. Then because a circle is a solid, the one of all the solid locations that define it, than we can measure its diameter.

- aera + of + a + circle (, United Departement of Agriculture, USA)

It suffice now to examine this figure to read and express the theorem of circle aera. This latter is directly defined in the space structure when the squaring a circle is resolved.

With AP = Space-Constant,
the aera of the circle (C) is there precisely equal to:

circle (C) Aera = (Space Constant).(2R)

Or practical expressed:
The aera of a circle is equal to its Diameter time the Space Constant.

- "area" equation (USA nj) - formula for "area" (USA nj)

This statement seems to be strangely an erroneous one.
However, it is exactly true! Why?

a) - Note that the squaring a circle can be done with the condition that the square aera is equal to the aera and/or the circonference of the initial circle. Therefore this above statement is a quite exact and precise one.
b) - To prove it, consider this next figure. This latter shows that the diameter AD of circle (C) is equal to it radius squared (R2).

- true basic (HongKong)

- perimeter of a circle (Canada, Ontario, Hamilton McMaster Univ.)

- demonstration + of + the + "area" + of + circle (South Africa, Cape Town, African Institute for Mathematical Sciences,

- circle "area" formula (HongKong)

- mathematical pi (, Wisconsin, USA)

- Regular + solid + whose + surface + area + is + 4 + Pi + times + the + radius + "suared" (, UK)

- mathematical algorithm morphing art (, Spain)

Actually. The universal Space properties are immutable. The consequence of which is being abble to morph in unbounded manners. In fact, Space is immutable as defined exactness in Changes.

- Africane Institute for Mathimatical Science (Ethiopia)

- MATHEMATICAL MODEL MECHANISM Deduction Induction (, Streetsville, Canada)

- rolling circle mechanism (Vietnam,

- model matematic (Poland)

- the + expression + TT.r2 + gives + the + area + of + a + circle + with + radius + r (, California, USA)

Aera of circle
Let us construct the square of side (AD') formed by the intersection of (C) with the unit axis (u). According to the Lamca theorem,
AD'2 = A(u).AD
In this case of figure we can write it as:
AD'2 = AD

The diameter of (C) is defined as equal to 4, its radius R is thus R=2.
With A(u)=1 then, we have AD'= OD'= R.

Because we have according to the squaring a circle:
aera (C) = AM2 = AP.AB = AP.AD = Pi.AD
with AP=Pi and also:
AD = (AD/2)2 = (AD2)/4
Thus, with AD=4,
circle aera = Pi.AD = Pi.(AD2/4) = (Pi/4).AD2

As the squaring a circle happens when the square aera is equal both to the circle aera and its perimeter then,

square aera = circle aera = circle perimeter
[(Pi/AD).AD2]aera = (Pi.AD)perimeter

- mathematical pi (, USA)

- Proofs without words area of circle (Australia, New South Wales)

circle Perimeter or circle aera
The Perimeter of a circle is equal to its Diameter time the Space Constant.

circle perimeter = (Space Constant).(Diameter)

While stating only the circle aera we get both the aera and the perimeter of the circle ones! Therefore, reading directly from the squaring a circle structure we get the basic complete two circle theorems as follows:

circle disk Aera
The aera of a circle is equal to its Diameter squared time the Space Constant divided by 4.

circle aera = (Space Constant/4).(Diameter2)

Note that space is a matter. Therefore, a curve or a line is formed by successive elemental matter. An elemental matter is a cube of unit dimensions. Then, any point of space is seen at least as a square. Therfore, a curve and a line is also an aera formed by successive elemental unit squares.

- mathematical "area" (, California, USA)

- person who figured out the equation of a circle (Canada)

This is the just and important expression.
Actually, until now notions of a circle are conventional and abstract ones. From there it throws up the irrational and transcendental number problems because it was stated that these types of numbers can't be geometrically constructed.
In opposition to these Mathematical opinions here in this text, the circle is rationally constructed with concrete space elements. Therefore and really, the circle can be figured out concretly from space.
In Dakhiometry it is proved rationally that ANY NUMBER as language symbols, that are no more than Matter Quantities, can be defined and constructed with space elements.
While matter is discrete in hyper-finesse, however there is no hole or no gap in a line according to the Succession Principle logic.

- "perfact" circle (Canada)

- Pythagorean Theorem formula for "stupid" people (Canada Nearnorthscools)

- calculus "area" curvilinear (Thailand)

- the + ratio + "og" + "thwo" + sides + lenghts + of + the + triangle + is + AB%3A+BC+is+2%3A5 (USA wednet edu)

May be, the ratio of two sides in a triangle is the ratio of the square root of this two sides squared.

- circle + surface (Israel)

The circle aera is a reality.
The basic reason is as follows:
Because there is a sphere aera and as a sphere is formed by successive circles then the logic states that; The sphere aera is composed of successive circle aeras

A sphere aera can be calculated with an algorithm using successive circle aeras.
Algebraic Integral calculus is only an approximation. There is proof using straight edge and compass that shows precisely a such aera construction of the sphere. From that, one can define any part of a such spherical aera.

Statement of the Space Constant

- mathematics is the language of nature pi (Mexico)

This is a Fact. The Space Constant is from the universal spatial language, the one of the life talking. Life talks when creating.

- give statement of pi (Bhutan)

The Space Constant is a more fertile basic space property than what is known with the Anciant Pi. This latter is only a means for measurement of a circle.

The universe matter space is a whole absolute precise locations for defining precisely any object construction according to structure and quantity of matter conservation. Without precise location in space, there is no possible conservation law. Space is not a passive property. In the contrary, space is the concrete reality of the universe Potential. We must keep in mind that any space location should be a means of potential measurement and its direct transform that is the Kinetic Energy. If there is no absolute space property then, there is no possible measurement of length, no potential and no means of measuring kinetic energy.

Therefore, if there is the necessity of an absolute space, there is also and necessarily, some Space Constant that play the role of scale reference. It is only the property of the universe Uniqueness Principle. So one should consider the result of the squaring a circle is to find out the most fondamental space property that allow to describe precisely a relatonship between circular realm and the linear one. The following Space Constant statement is to underline the absolute discrete placements of elemental locations allowing the whealthy of forms in the universe.

- physical meanning (Egypt)

- transmutation circle (Slovak Republic)

- pi + needs + to + be + accurate + to + define + a + pie + chart (, Uk)

The Archimedes' pi is accurate within 1/10 (3.1...) what ever are the decimal digits of a computer used.

Why is it fundamental to name the Space-Constant?

- Pi + the + breath + of + the + universe (Australia)

In Fact, there is nothing else than the Space-Constant. The Pi is only man anecdotal history.

Here is why it is rational to be in consciousness of a Space-Constant.

Space-Constant is constant

The space-contant is explained all along this text. However practically nobody means it.
Here on this next figure it is proved why a space-constant is constant because it is the reminiscent of the universe Permanent principle. In fact the space-constant is a direct avatar of the absolute space structure represented by the circle/square system.

From the absolute space the cercle/square structure is immutable. this means that any ratio between circle and square points that are refered to the common center, is a constant whatever the scale of this circle/square system.

Any ratio from the circle/square is a Space Constant !

Particularly, the two caracterized circle denoted as (C1) and (C2) are representative to this structure constancy.
The ration (AC/AD) represent the space constancy of circle/square system.

In any figure scale, there is the identity according to the homothetie of circle/square system.
In any space scale, the circle/square system is a constancy in their form ratios.

With AD=4, the space-constant is written as:

Space-Cst = (AC/AD) = (3.1201937.../4 = (Pi/4)

where (3.12019...) is the new value attributed to the so-called anciant Pi.

This figure show why in any figure scale the space-constant is truly immutable and consquently the Space-Constant is a true universe Fact.

It should be noted that the two circles (C1) and (C2) is the proof that the square-root of 2 is a Constant.
Therefore, the (square root of 2) is a rational quantity because a constancy is necessarily a rational precisely determined value.

Therefore, the Socrate's incommensurable unit square diagonal is only the proof that the space constant was still ignored.

- prove square root of x (, Bresnan Communication, USA)

The Dakhiometry proof of square root construction is yet done! However, because of the coagulated Pythagoras' theorem maniac, no mathematician have some insight into it.

Statement of Space-Constant TT

Constructions in space are done in successive locations with two characteristics. There are two independent space placements: the linear and the curvilinear.

Relationship between linear and curilinear successive locations in lines, are in ratio related together in proportion with the Space Constant denoted as TT. The two characters T means Transmutation. This latter is an unique key for the possibility of equivalence between linear and curvilinear figure.

Constante de l'Espace

Example of curvilinear aera (S) of circle
and the volume (V) of sphere:

TT = 4[S/(D2)]

TT = 6[V/(D3)]

- is r2 TT the same as TT r2 in the formula for the area of a circle (, WILDBLUE)

These above (TT) for aera and volume show that space is characterised by two realms that are the Linear and the curvilinear oneS. As space is the universal unity then it must be some relationship linking these two space forms. A such something should be universal and should not be particular arangements in space construction.
It is why this space unity is the simple spatial constant denoted here ad the (TT). This is a new concept that has nothing to do with the Anciant Pi attached to the difficulties of measuring a circle.
Aside this theorical statement for the Constant (TT), its uniqueness is also illustrated in practice. It can be proved in Dakhiometry that this Constant can be discovered in a linear spatial structure without any circle. Therefore this next raltionship:
Space Constant

can be given by the structure used by the "spatial calculator" of the Dakhiometry. This latter is only a linear structure in a square inhreited from the squaring a circle. The calculatore needs not the necessity of using any curvilinear tools as surface and perimeter of a circle.

The (TT) is really The Universal Spatial Constant.
It has a wealthy consequence when it is understood. Because if universal laws are expressed only in a Two Dimension Planes, any 3Dimensions volume needs the necessity of a mixted Linear and Curviliear unity. For example a planar latice of a solid can be stay in a plane, the whole solid can be formed by other latice planes that can extended in any other direction.
Thus the final solid is necessarily a form of mixted linear and curvilinear types. Therefore, the construction of the universe objects is possible only according to this Spatial Constant, denoted here as (TT), that allows the coherence of space unity.
It is why knowing that, the Dakhiometry can define and state simply any solid volumes. The old mathematician Pi is a too poor empirical concept and can define volume only through analogy with some few linear solid forms as did Archimedes when trying his Famous Method.

A more logical statement

- birth + of + a + square (India)

The circle transmutes in structure to reveal space elements in possible conscience of measurement. This is the birth of a square the Anciants denoted as the life birth. The meaning of the squaring a circle from that measurement conscience in space was possible. Therefore, the statement of the squaring a circle should be as follows!

The linear space is from a curvilinear transformation. It consists to correspond successive points on curve to successive points on a straight line. This equivalent transform is defined according to a Space Constant (TT), as following:

Space Constant

Examples of curvilinear aera (S) of circle
and the volume (V) of sphere,
equivalent to linear diameter (D), as:

TT = 4[(S)/(D2)]

TT = 6[(V)/(D3)]

Consequences of these precise definitions of circle.

Aeras in circle-square structure
We can now define the differents aeras in a circle-square structure as the surface elements (a) and (b) show on this next figure.

Let S the square total aera.

The total aera parts (a) of the square aera external to the circle one is:


Thus, the total aera part (b) of the circle is:

s(TT/4)-[S(1-TT/4)] = S(TT/2 - 1)

Their perimeters are also directly defined. More complexe aera may be tempted according to the following example.

- federation square structure (Taiwan, National Chiao Tung University)

Aeras in circle-square structure With these formula we can verify that the aera of square of side 4 is equal to four time the aera of square of side 2.

By adding the yellow and the cyan colored aeras in the little square of side 2, we can find their total as equal to the aera of side equal to 4.

Note that with the classical Pi=3.1416, it can not be done a such equality.

The usual Pi and its related Diamater is only a simple particular recipe.

Because it is the Dakhiometry's Space Constant, the Squaring a circle is a space gate in the universe.

- mathematic (Viêtnam)

This world is chained up by an old Pi trick. Here is a conjecture that can be resolved true with the Space Constant cencept:

Can you resolve the Squaring an ellipse?

It is a problem resolved as true by the Dakhiometry with straight edge and compas. Youn can't escape from it according to any impossible theorem.

This whole world is outmoded idea with a general erroneous Pi warranted by any calculator, while the reality of precise science should get into the Space Constant concept.

So your duty is to try resolving the following problem:

The squaring an Ellipse.

- tangent + passing + simultaneously + through + Parabola + ellipse + hyperbola (

These figure are wholy inscribed in the space structure. They can be constructed precisely. Therefore, a common simultaneously tangent at these sfigure can be determined by construction.

- ultimate + value + of + pi (USA)

So I will soon do the proof of squaring an ellipse. It shows how form transformations need the Space Constant.

- prove tangent circle ellipse (Spain, Universitat Politechnica Catalunya)

This a new marvellous consequence of the Space Constant.
After resolving the squaring an ellipse, the problem of a tangent to an ellipse is directly the one of a circle. Therefore, from any given point exterior to the circle, tangent point of a circle is the coresponding point for an ellipse. As we know how to construct a tangent to a circle we can immediatly deduce the tangent point on its correspondent ellipse. This is done by simple, easy and precise spatial construction.

- space constant (USA Illinois)

You will see that the space constant is a most usefull key for understanding the solid form.

- Surface d'un segment de cercle (USA mil)

Je le vous dirai lorsque j'aurais exposé les surfaces et les volumes des solides, après les avoir justifié sur des fondements. La Constante de l'Espace, y joue un grand rôle principal.

- measurement + "og" + common + geometrical + forms (Hongkong)

- qu'est-ce + que + exprimer + la + longueur + 1 + d'un + cercle + comme + fonction + linéaire + de + son + radiuson + R (France)

- un cercle de 0 degrees (, Canada)

Mon œil.
Même en géométrie des parallèles se rejoignant à l'infini, on ne peut faire de telle prouesse..
Maintenant, essayez de tracer un trinagle de 60 degrés en tout, somme de ses trois angles, vous verrez que vous ne pouvez plus dormir. Cependant, un cercle de 60 degrés peut se faire dans une Géométrie où l'angle droit est égale à 30 degrés. Essayez d'abord de fabriquer une telle Géométrie... où l'on perd non seulement le Nord mais aussi, son Latin. Il est possible que le jour où le mathématicien, las, avait renoncé à monter une telle folie à 30 degrés et après avoir vidé toutes ses bouteilles à 55 degrés seulement, qu'il se résignait à revenir vers sa Géométrie sagement sphérique.

Perimeter of a Perimeter unit of a circle
On this next figure is represented a length of Space AP.

Squaring a circle of perimeter unit will give necessarry a Unit of straight Length.
Thus, with this unit Length=1 a circle perimeter=1 and diameter (2R) will gives the value of the inverse AP as:


It is here, only a particular case construction because in Dakhiometry there is a general compact and precise structure for doing the four basic operations for construction. Negative length are only conventional definition of a line and a plane divided into two parts.

- can't divide by zero (Missouri, USA)

Effectively, A universe Principe can be founded on.
A Unit Length is an eternal being... it is also the case for the circle of perimeter Unit.... The unit-square is always valid whatever are the Circle AP dimensions.

There is never Zero division according to the Elemental matter as a Permanent Matter Unit. The Elemental matter Dakhion is from the Universe Permanent Principle of the Discretness of Matter. Conservation Priniples rest on such Universe Discretness of Matter Foundation.

The Dakhiometry Spatial Language rest on the Lines, Curves as formed by continual successions of elemental Matter. The Principle of Lines and Curves is that they are formed by Elemental Matter Dakhions. The Dakhion is defined as The-Preceeding-Succeeding Element. With such base any complex constructions in the universe can be understood as formed from such Property of ONE DAKHION as The-Preceeding-Succeeding Matter unit. This is the characteristic of dynamic Active Matter Element for unbounded Construction in the universe.

- exhaust planes construction (Brazil)

- construct the inverse of a length, geometry (, Texas, USA)

- Complex Elliptic Inverse line (Singapore)

- the fully elliptic differential governing equations (Philippines)

- Singapore (Indonesia)

- i divided by zero (, Quebec, Canada)

The solution here is a true one according to the theorem of the circle always defined by three points.
When three points are on a line then this line is the maximum circle of the universe with the maximum universe length as diameter. When this three points are on a same location then it is the ultimate elemental circle.
The theorem is:
Three points define always an unique circle because they define the total space directions.

Practically it appears as:
a) - By its form any three points define an unique circle.
b) - The total inside angles formed by any three triangle sides define an unique circle.

- dvide by zero (Denmark)

This is the result of rational spatialconstruction that rests on the basis of the circle as 3-points.
Also, for example, the consequence of this theorem proof gives rise to the simple spartial explaination of the Morley equilateral tri-sector in a triangle.

- 1 divided by zero equals infinity (Philippines,

This proof is really a valid one with the Dakhiométry spatial construction.
a) - The Dakhiometry universe is discrete matter.
b) - First, it is proved that any three points determine a given circle.
c) - Then, three aligned points determine necessarily The Determined- Circle or the Greatest rational universe Circle.
Because the universe is discrete then, it is more just to denoted this circle as the logic of the Great universe-circle. The Infinity is an old Anciant notion when they ignored that the Space is absolute.

Proof of (1/Zero) as the diameter of the Great Universe circle diameter

The shortest proof but he most basic logic one rests on the universe discrete absolute space. Space is Distance and Direction. According to the curvilinear succession of space points the law is stated as follows:

1) - Two successive curvilinear points (A) and( B) determine any circle passing on this two points.
2) - A set composed of a Third successive point (C) to the first two successive points (A) and B), determines an unique circle containing this set of three successive points.
According to the succession principle applyed to the curvilinear line, a) - Any third point (P) in the sucession chain to the first two (A) and (B) successive points determine necessarily the unique circle (ABC).
b) - Consequently to the property of a curvilinear succession chain, Any three points in curvilinear succession, determine an unique circle

The logic property of discrete point succession is then use to prove that the Universe Great Circle is also rationally determined according to any three given points.

- circles inside giant circle-circumfrence (, Michigan, USA)

Inverse of lengths

On this figure, is shown that 3 points A, B, and C difine a circle circumscribed to them.
As a circle is a total of 180 degrees of Directions then the total 3 angles of a triangle is necessarily equal to 180°. This property of 180°, is used to prove how to determine the Universe Great Circle.

On the left of the figure, let ABC a triangle inscribed in a circle. It is shown how the three angles (A, B and C) can feel the total 180° of a circle. Note that the total circle direction can be conventionally define as any given value. But the real total discrete points of a circle can be the gratest of the universe points quantity. It is a currently bad defined as an uncommeasurable Infinity. However, the Dakhiometry define this so-called uncommeasurable Infinity by the ratio (1/zero) quantity.
For 180° angles definition of the triangle form it can be written as the arcs lengths BA, AC and CB. Thus:

arcs (BA + AC + CB) = 180°

At the figure rigth is shown how to define the universe Great Circle by choosing 3-points (A, B, C) on a line. It can be seen that "line" (ABC) should belong to the universe Great Circle according to the above law.

Because the total angle defined by this cyclic 3-points is:

(arc BA) = 1 element-point
(arc AC) = 1 element-point
(arc CA) = 180°

arcs (BA + AC + CB) = 180°

This is the circle central symmetry characteristic of total direction. It traduces the cyclic of the circular-succession that has neither Beginning nor Ending.

A) - A, B, and C define necessarily a circle according to that three-point in curvilinear succession define one unique circle.
B) - According to the following theorem of inverting length, then the ration (1/zero) is necessarily the Greatest Circle diameter of the Discrete and finite universe.

Important property
At the universe scale There is no more distiction between linear and curvilinear mode. This a logic consequence that can explain why the immutable elemental matter activity is done along a straight line. This allows to state that the electromagnetic action comming from far away stars hit the Solar system in perfect straigth line manner. Only refraction in media can deviate the media light phenomena.

- discretness (Ukraine)

- Exploring Arcs, Chords, Secants and Tangents (Philippines)

- modernism unique spatial object (Australia)

- divided + by + zero (Mexico)

- result + prove + unicity (Philippines)

You justly see it.
Univers Fact is the expression of Uniqueness principle. It is the base Reason of Physics to understand that matter is necessary existing in Discretness of its Elements.
Equality is not a man's artificial simple talking word. Because matter composed and formed from a same matter Element, denoted as the Dakhion, is the foundation of human's Equality concept. Univers is a Whole of matter Elements. From there Uniquenes of the the matter Element imply that Uniqueness has necessary the Permanence property.

Note that it is the consequence from the fulness reason of the Uniquenes as follows:

1) - Necessarily, the Reason of Unique concept is not in two or in many Forms as Existence/Or/Non-existence.

2) - Therfore, a Unique has then necessarry and stricly the property of One-Existence.

It is why from this basic Reason,

Note that whithout a such foundation, Knowledge is impossible because this man's capacity of knowing rest on the EQUALITY Principle. It is why man's know how to Count. Counting rest on the Unity principle. Counting Unity rest no more than on the basic Fact of Discrete Matter.

- Zero + in + mathematics (..)

Considering the discret universe fulness, there is the no-abscence-of-matter. The first quantity of matter is one elemental matter. Therefore, there is not a Zero-Quantity in the universe. The presence of matter is from Permanent principe.

In algebraic mathematics method, the Quantity is represent by a language symbol denoted as Number. Converted talking language words by Numbers to any quantity had difficulty when one need to represent larger amount of quantity that a man can have a practical access.

It is why the problem of practically using Numbers to represent any possible quantity need to invent practical symbol of defining how to represent Number for great Quantity because it is impossible to invent a great amount of conventional words to represent any great Quantity of the universe.

Finally it was invented in Indian the conventional symbol that allows to define a rule for representing Great Quantity. The symbol is nothing else than the one that allows to use an amount of words that can be use in cyclic manner. This symbol is like the clock that is abble to indicate hours all along the unbounded Time. Thus, for counting Numbers it was the Indian Zero invention that allows to write withh some simple symbol to represent any great possible counting.

The Zero is therefore, NOT-A-NUMBER.

The Zero is only a symbol mark on a clock cadran that allow to represent any great quantity of Time while this concrete mark has not any Time property.

- divide + by + zero + jokes (Australia)

The basic reason for any science is that the universe is the one of Discrete matter.
That means if there was not any matter then there is no universe because the universe matter is a Quantity et not some nothingnesse. The ultimate matter is at least One Elemental matter. This latter is necessary this elemental quantity.

Therefore, the space a composed by elemental Point, Line and Forms is at least define by One elemental Quantity.

The Zero is only an useful but conventional symbol that allows to define a mode of cyclic counting of quantities. It is then an illusion to divide a Number by a Zero as Not-a-Number. This transformation between quantities should then be a coherent and homogeneous one by matter-interaction or mutual Quantities-Interactions. The ultimate of a possible division is necassary the divided-by-an-elemental-quantity and never by a Zero-as-an-illusion-of-quantity.

The Proof of Absolute Space

- what + is + a + contradiction + in + math (, Texas)

Science should rests on the Absolute universe space of the Discrete Matter. In the universe, any objet is always defined at least, by one element of Matter. There is no object of Zero-Matter. This is the principle of the universe Absolute Space.

And the absolute Space can be rationally proved as true.

How do we do to get this rational proof?
Even if it seems that anything in the universe are alway changing and that anything is appearing and vanishing in motion as life and death evens, the Absolute Fact of the universe space can be rationally proved.

This proof of the space Absolute property consists to rationally define that there is, at least, only One-Fact-of-Matter-Permanent-Property in the Space.

This basic prof is yet already done!

This is done according to the Determination of the Space Constancy that allows the universal transformation between two basic Forms as the mutual transformation between Circle and the Square.
This isreally the mains aims of the squaring a circle resolution. The so called old "Pi" is only a secondary consequence among a lot of another ones.


According to this proved Fact,

1) - As any object reality is at least defined by the minimal One Matter Element.

2) - Then, there is no Zero of Matter. Therefore, the continuity of matter construction is the rational fact of the universe reality. The construction are always the possibility of matter transformations according to the processes of (Addition, Substraction, Multiplication and Division).

3) - There is no impossible matter-transformation according to the universal laws in the whole universe. Paricularly, there is no impossible Division by Zero.

In conclusion
The Zero-is-not-a-number but only the ultimate one elemental matter: the dakhion. This give rise to the definition of the minimal One Point that necessary constitutes Lines and Curves in the Space.

Inverse of length

Inverse of lengths
This construction is directly derived from the Lamca theorem. It allows to state an usefull theorem for inverting any length AP!

On this next figure, are done the inverse of circle diameters length (a, b, c, d, e).
These constructions rest on a reference by a unit circle.

Theorem of inverting length
Let a first unit radius circle intersecting any other second circle.

Projections of these two circles intersections on their joinning center line, determine with the unit circle center, the inverse of the second circle diameter length.

- Divided + by + Zero ( Florida)

The fundamental principe of Matter and Energy Conservation and the Discretness of immutable Elemental matter imply that there is no ghostly interaction in the universe.
Therefore, the Zero-Matter is only an illusion.
The Zero is from human language convention to signify "Object-Out-of-the-current-convention". In fact, this "out-of-convention" is also an Object and don't means "a-Nothing".

For the Number system, the ZERO is useful only to delimit the series-of-Counting-Numbers Zone. For example:

(Zero, 1, 2, 3,..., 15 Birds)

Should be conventionally understood as:
(ZERO-Bird, 1, 2, 3,..., 15,... and ZERO-Bird)

... and obviously: Cats is not there taking in account.

Zero is then only the usefulness as the delimitation symbol of a Counting Zone.

Therefore, Zero is not significant as a NOTHINGNESS... because there is no Gohst-Matter in the Absolute Discret Matter of the universe.

ZERO-as-Nothingness and then imply the INFINITY OUF COUNTING, for example the Euclide's Line, contradicts the universe immutable Principle of Energy-Matter Conservation.

- inverse ++ power + mathematic + equation

In Dakhiometry, The Lamca theorem is also the direct basic reason of the circle power point theorem proof.

One can see that with all preceeding tools it can be done yet many precise constructions in space.

- definition of a line (, USA)

Actually, theses constructions are consequences of a line definition.
A ligne defined from Pythagorean Numbers as (1, 2, 3, ..., n) that gives rise to the Euclidean line is not really a definition but a dream coming from empirical sensitive image of line. It is the case for a line unclosed by two infinities. These latter are virtual and empirical concept that rest on no reality fact.
Therefore, a line should be real when it is defined by its two ends. It was the Aristotle definition however it is concerning only for a segment of line.

The exact and precise definition of a line is:
A line is formed by the succession of discrete points situated between two end points.

This next figure concerning the inverse of a length, is in fact how to figure out any line.

This is to tell that there is no Segment of line.
For simplicity of language word one can named a length as a "Segment". But we should be in consciousness that it is only a Line.
According to the Pythagorean Numbers the curent Numbers theory gives a false concept of quantity. In Dakhiometry it can be shown that any segment contains the possibility of designating all the universe quantity until the discrete ultimate elemental point.

The Line of modern Real Numbers is only an empirical inheritance of the Anciants misreading about space line. Also, the Real Numbers Line is a bad construction because it is defined by a convergence method as was done by Euclide and Archimedes exhaustion method. The mathematician infinity is in fact born from these convergence methods as a conventional approximation, wellknown: "converge to a no touch taboo".

- how + could + you + find + the + circumference + of + many + circles + with + a + calculator + without + entering + 3.14 + for + every + problem (USA Alabama)

At first, the 3.14 is an erroneous value of a quite false mathematic product.

The principle in Dakhiometry and not the one of mathematics, is as follows:

1) - Any measurement of figure must start from a circle definition.
2) - It is necessary from that to define a square.
3) - Then from a square, one can define the measure of ONE circle.

Now we can proceed to choose and to define this circle as an unit circle.

From this circle characteristic and according to the Dakhiometry space transformation knowledge
Everybody can now measure any other circle, as a proportion of this unique previous defined circle without using no more the Space Constant TT!

This is the universal magic immutable Space Constant property

Note that all this new method remains quite inefficient even if one use the most Famous of most Great Anciant mathamatician invention, the Famous Number 3.14 of the Great Modern Conservative human though. Unhappily, independently of any reason, everybody is "free" to chose to what he want to obey to.

- corresponding + lengths + in + similar + figures + are + given.+ Find + the + ratios + (Figure+A+and+Figure+B)+ of + the + lengths + and + areas. + then + find + the + unknown + aera. (USA Georgia)

- the mathamatical country problem (Canada)

- human memory capacity (Slovak Republic)

Important Remark
One may note there, that spatial language is the most simple. However it needs the capacity of an overall vision of space to be abble to discover the wealthy basic space structure.

In a such figure, any square can give any rectangle of equal aera. Thus, the segment AP is of any length. That is to say: may any length AP be a Space-Constant?

Actually, any chord AM squared can be equal to AP.AD.
However, the Space-Constant needs the condition of equality between the square and the circle (C) aeras. And according to the construction of this Space Constant as a tangent to a defined circle (C1), this latter is precisely unique. Only this uniqueness of the Space Constant allows exactely the equality between the circle (C) and the square aeras. The final result of these analysis is to give the basic proof of the Uniqueness of the Space Constant.

Therefore, we state a basic theorem proving that the squaring a circle is unique according to the uniqueness of the Space Constant.

In the circle-square structure there is one and only one precise unique length that allows the direct unique circle to square transformation of same aera.

This length is denotted as the Universal Space Constant.

Although the spatial language simplicity it can be seen that the circularity of the universe Permanence, is of great complexities with all the reasons that are related together for the understanding of human though.

- "indution" + cooker + pi + and + pi + than + stop (Singapore) - the value of pie used in maths (India)

Unhappily, all of this Planet world are yet practised the millenarry immutable an indestructible old erroneous Pi value...

- show me three hundred square root length (USA hr)

Heve you never seen somebody drawing a length of 300? Never, because 300 is a language numeral symbol.

However, the sqr(300) length is the one of sqr[(3).(100)] or sqr(3).sqr(100).

a) - It can be found by homothetic transform of the whole sqr(3) figure by Thales ratios.
b) - The Dakhiometry spatial method allows directly multiplication and division oprators.

- the + inverse + rotation + of + a + square + to + suffice + to + compute + any + product (USA Chicago)

- universal root (USA west)

Actually. What can be geometrically constructed was defined as a rational number. Therefore, every number is rationnal because any of quantity can be spatially constructed.

- math symbols - square root of 3 (Hawaii, Brigham Young University)

- an irrational length on the rational line (UK Canterbury ac)

- principle square root in math (USA Maine edu)

- the square root of three is one point (USA berry edu)

- rational square roots (India)

- algebra square root of, pictures (USA, Conecticut University of Hartford)

- "sqaure" root of three (, Florida, USA)

- drawing square roots (, Lewis University, USA)

- radical is an irrational number square Socrates (comcast, Texas, USA)

- wawe do (Vietnam, w642h/q42008/2009/)

- wawe do (Vietnam,

- - write + two + rational + and + two + errational + number + between + squar + root + 2 + bnd + squar + root + 3 (China)

Square root of 3 rational
Actually. This figure shows how to spatialy construct the length of quantity equal to square root of 3. We can do it with any length number of the universe.

In fact, anny quantity can be spatialy deternimed by a length as distance between two precise points. Therefore, any universe quantity, tell as a Number, is precisely a rationnal space length.

Until now, if there are irrational numbers it is because of Euclidean Division characteristic that is the never ended exhaustion method which can't drive to a precise number value.

- wawe do (Vietnam, w642h/q42008/2009/08/)

- roots of unity (USA, California, Montery College of the Desert)

This next figure gives 2-root(1)=1.
Also there is a same construction that give any root of number below 1.

- how do i calculate the distance between two points on a straight line when we have the point a =root x1 = -14 and b = root 2 = 18 and the mid point of ab =16 whats the distance between om on the straight line ox (Australia)

- Proof + The + square + root + of + three + is + irrational

- square root with compass (Belgium)

In the discrete continuation, any quantity value from Zero to unlimited quantity can use a compass to get its square root. On this next figure, it suffices to construct the diameter of a circle using the given quantity value. Then a square is determined the side of which is the square root of this diameter. The square is constructed at point Zero and with the circle intersection at the vertical axis located on the value 1 as shown on this figure for the square root of 3.
In Mathematics, it was defined that any geometric construction is rational. Therefore, in the discrete continuity of a length exhaustion, one of many theorems on rational quantity is as follows:

Theorem of rational quantity
Any quantity value from zero to unlimited ones, is constructed with a circle and is quite rationnal. There is no holes in a line

Note that this theorem rests on the basis Lam-Ca theorem.

- square root of five (USA Virginia)

Square root of 5 is done as for the 3 one on this figure by replacing the length 3 by the one of 5.
Square root of decimals are done with the same construction. It is because the decimal convention is only the homothetic for language of numbers. Number Languages are necessarry full of holes due to the impossibility to conventionally name the so numerous objects in continuity of space. While spatial homothetic property is recurrently continous even if space is discrete. The recurence principle is a principle of continuity of no-hole space-reality.

- square root in digital technology (Budapest University of Technology and Economics, Hungary)

Digital technology is formatted by the usual means of Mathematics for calculations. Mathematics know only a few ways for calculations. There is the two main modes that are the Pythagoras' theorem and the sine-cosine trigonomic functions. They give quantities as different dichotomic Numbers not being in continuity. This dichotomy is there called as irrational numbers.
It should be noted that in Dakhiometry, calculation of quantities are represented by spatial structure. A lenght resulting of calculation is found as a length representing directly a quantity. Length are there formed and delimited by continuity of discrete points. The square root of quantities are then directly given in space structure.
While with the Pythagoras's theorem it is given always as a squared or an inversed square numbers.
To be wholly precise with efficient calculation as in Dakhiometry, one needs to surpass the usual mathematical though of understanding the quantities in the universe.
Digital technologies for calculation are useful. But transposing calculation mode of space structure should be developped differently from the above a little simplistic methods used in Mathematics.

- does + a + circle + have + a + surface (USA)

It is a basic questionning. Do any line and any point have a surface?
Because the Ancients believed that Geometry was human invention and that any form is human mind product, Euclide had defined a point as an dimensionless entity. This was the case for Dedekind where Infinity is "proved" as his mind production.
However, the basic universe logic is necessary the Permanent Principle concept with the discretness of matter. A Permanent universe state should have the property of an absolute defined matter as the universe Space. Because only an absolute defined space can have the property of location. From this base it can be understood why there is Forms and how to have conscience on it by Measurement. Because of the conscience property by measurement, an absolute universe space is necessary a finite quantity. Human consciouness and measurement is necessary an acknowledge on a finite quantity. We note there that our conscience is the space construction and consciousness inherits the space property. Therefore, a discretness principe in a finit space, is necessary a discrete surface quantity in a discrete location for centering it in a whole defined space.

From these bases we can see that a dimensionless point can never be located. Thus it can't be measured because dimensionless point is unconsciousness and can't never be measured. The dimensionless point is the consequence of the Anciant' incapacity to know what is Space.
From a such bad foundation of space it grew the Continuum belief. And many examples of indefined space can be seen when Mathematics proved that "a Part is greater than a Whole" and also, the modern difficulty of defining the Real Numbers set where dimensionless point leaves a line made of holes from where Mathematics created the so-called many difined Infinity Sets. With the incapacity of knowing what is space, the old and modern Mathematics have no foundation to be classed as advanced sciences.

With the Dakhiometry one needs to be in acquaintance with the discretness of matter space. Any point and any line or curve are surface defined as object realities.

- why that counting's rational irrational are called Real numbers (Philippines)

Human have the skill for rhetorical figure of speach.

- root (USA California)

- root + 3 + rectangles (Canada)

- bankruptcy in integers (, USA)

Weird and false things are the irrationnal numbers!
You are invited to produce the hexadecimal integer series with a famous irrationnal number as the basic unit:

Irrationnal number
It is the famous irrationnal number that is to say the argument of the geometrical impossibilities of the squaring a circle and the doubling a cube.

Here is some examples:
With (n) the Natural Integer series from 1 to unlimited value,
Irrationnal numberto hexadecimal integers
Now, consider this following given equality:

Then, a series of the irrationnal (H) correspond exactly to a series of multiple hexadecimal Integer Numbers as follows.

Irrationnal numberto hexadecimal integers

Logics proof:
There is the real fact of Narural integer Numbers. Although Rational and Irrational numbers may be mixed on a line, these two types of number worlds are necessarily incommunicable between them.

If one can produce from irrational numbers some rational ones then, one produced there a contradiction to irrational numbers. The above examples show this contradiction. Therefore, Irrationality is only a FALSE FORMALISM.

This proves that there is a quite FALSE and virtual Irrational World built by Mathematicians with a False Euclidean Division method. This latter confusion gives rise to the current Irrationality Belief.

What is irrationnal...
is precisely the Human Irrationality Concept characteristic!

More serious:
This whole current World is guilty to be blind continually on all the rational reasons of science exposed by the Dakhiometry.

- how to count square root (Sweden)

- root square (Japan infoweb)

- straight edge square root (Netherland, Universiteit Twente)

Actually, any number of different series types can be applyed with this Root-n following formula as square root.
The following formula is under usual Algebraic form however, it can be spatialy constructed in figures. This give the best proof of rational and precise constructions for any length quantity representation. There, any line is really precisely the continuous formation of space quantity.

- triangular math root (Bulgaria)

There is here also three data for an equality equation.

- irrational + square + root + unlimited + precision (USA WOW)


According to the current Theory of Numbers,

A Theorem of
Any Root n of Number (x), is statted as follows:

Irrationnal numberto hexadecimal integers

a) Where (n) is the Natural Number series form 1 to n.
b) And (p) is any number.
c) (Root p (x)) is noted as (root-with-exponent p of (x)).

Calculations Examples :

Example 1) - With x=9, p=15 and n=7

Irrationnal numberto hexadecimal integers

For Any conventional Number,

Example 2) - With x=7.51, p=11.75 and n=5.3

Irrationnal numberto hexadecimal integers

Pay attention:
It is there not a pleonasm. Because in Mathematics, an irrational number [root p (x)] is defined as a particular number quite different from an integer x.
Mathematician should define two different numbers:

(y)=[root p (x)], is an unknown trasformed from (x) through [root p (x)] according to some approximation Exhaustion and Convergence method.

Therefore in Mathematics, [root p (x)] is not the same x find in [xn].
For example, with mathematics irrationality as conventionally defined, it should be necessarily a difference as follows:.

Irrationnal numberto hexadecimal integers

Really, if one find an equality between an Irrational number and an Integer one,
it is the proof that the famous Irrational Root of numbers is directly and concretly related and belong to the Rational Natural Integers. Therefore, there is not Irrational Numbers but only a bad Euclidean mathematic division method based on Exhaustion search.

Main conclusion in brief

Irrationality is not an universe fact.
Irrationality is only mathematicians' language ignorance of how to interpret the discrete Matter Continuity

- quantique + dakhion (France Poitiers)

- take + a + line + and + form + it + into + a + circle + pi + is + missing + space (USA Washington)

There should not some missing space. If there is one, it comes from approximation practise.
The counting Because the squaring a circle proves that there is Conservation of Space between the square S and the circle C. A Space Conservation is the meaning of equality between the two corresponding surfaces. Only the different arrangements of elemental points provide different lengths for their perimeters as:
[4.D] different to [Pi.D]
where 4>Pi.

- What + is + the + importance + of + Pi + 3.1415 + in + business (USA Tennessee edu)

The most fondamental reason of using constant reference is to choose of exact one on which all the universe laws should rest. It is the human science purpose because of its universallity reason of life reality.

However, human though is no more reaching a satisfying level to be abble to determine what are the basic of universality in law. Therefore we are all on Earth to use no-exact sciences but generally conventionnal empirical and mechanical processes determined by the practical science for everydays actions.

In such situation, an example is seen in the case of the old Pi value of 3.1416. This latter is only an empirical value the truth of it is only validated as sacred value according to some traditional artificial mystery maintained by dogma.

The real value of the so-called Pi as a simple particular mathematics problem, is only how to find a trick that allows to give approximately a sufficient length value of a circle for practical measurement. On it there was fantasy of mathematicians that try to give some mathematical formalism to a Pi empirical value. It is why we can see many numeral processes formulating a Pi value the truth of which is according to the belief of somme mystery on which are founded Numbers.

The Pi was and is nothing than an empirical formalism replacing the human ignorance as the exact universallity of the world.

The truth is reached only when one can get what is the real conscienciousness of the physic around him. The most basic material presence that can never vanishe is what everybody can be sensitive. It is the material Space. Therefore, being conscious of the space is to know how to measure it and to act with and on it. We denoted it as the fundamental universal language of space. Because a real basic of language allows to exchange, to transform in uniqueness and multipilicity system.

In the case of understanding what is the basic importance of this space language, one get some basic characteristics that space is a whole. And being conscious of the total independence between rotation and linear movements in space. A real human science should be consciousness that in a whole space there should be some basic factor inscribed in space that links these two independent movements in a unified space system. In basic space language we tell that there is something that unifies the circle with a line or a square.

Resolving a such problem is telling as how to square a circle.

The solution of it gives to us a real basic factor of matter transformation universally used by the matter laws of the universe construction.

The resolution of a such facror is a precise value given directly the True, the One that whe should denoted as the Space Constant! Aside as such mode of resolution and a such founded value, there is only an abyssal of human ignorance.

It is the case of the Pi=3.1416 value, "universally" used by sciences and more badly, by the business world. The absolute error appears in the use of the old Pi and is of 0.7%.

Why it is bad for business?
Business is money. Money is only a product of calculation. Business is governing the human life. That is to tell, with the old empirical Pi used in their calculation the world is erroneously calculated. Precisely tell, our life id baddly and erroneously estimated. What is the value of an 0.7% absolute error done on a simple tiny billion of money of a very poor business?

The real effect of a such error is however governed by the universal Conservation of Action. This means that aside a great deficiency for one, in the other hand, there is a great profit for the other. A such unbalanced world may be conscious or unconscious for practical business activities. However, it is only a real chronic disease for life of all.

- history + of + mathematics + THE + PI + EVERYTHING + CONTAINING + PI + WHO + INVERTED + PI (South Africa)

- formulas + with + include + pi + give + the + formulas + in + symobols + and + tell + what + it + repusent (USA)

All of statistic mechanics use the Pi. Examples are given with the Gaus, Fermi, Dirac, Bose, Einstein, Maxwell, Bolzman,... ect. This Pi come from integral and trigonometric functions where one uses mathematic developments in calculations. All the modern particle sciences use an erroneous value of the old Pi.
I have no other comment about the exactness of these science methods.

- trig functions and ancient pyramids (USA)

Trigonometric functions and the old empirical Pi currently used, are the two main errors meet by the Trigonometry. We must add to these errors the imprecise Euclid's division algorithm when performing these functions using Number calculations.
Note that it is proved in Dakhiometry that a sine curve is precisely a paraboloc function.

The determination of Trigonometric functions doing with a circle and orthogonal axis is really a dummy formalism. The Trigonometry gives only approximative results.

It is why what do we think about the modern Algebraic calculation methods of convergence and function developments where the Trigonometric functions are intensively used? This is the case of the Mechanical Statistics found in Quantum Mechanics.

What is the form of an elemental immutable matter?

- can pi be constructed with a value of three (USA Florida)

It is rational and also most intersting to seek an answer for a such issue.
During the first time of a human practised techniques, he was yet meeting the everydaus problem of how to ajust a circle to a linear solid. The wheel is never beeing invented. Rotating and linear motion are the natural spatial characteristic of the alive movements and any alive have to manipulate curcular and linear solid forms. For example, everyone may experience a fall during that he is rollong on an inclined plane with his whole body. It is there that practically, everyone had invented the concret wheel running.
Even that one had skill to construct anything needed but his sciences of measurement was not yet precise. Therefore construction use mostly empirical recipes of defining solid forms. Adjusting a circular form to a linear one can be done with some approximation that run well for coarse needs. Thus, at the anciant time it was more easy to remember that a circle perimeter length can be conventionnally equivalent to three times its diameter. From these usual practise the circle perimeter as a proportion of its diameter remain until now. Because nobody can tell the exact means to measure a circular line then, the corresponding of a circle perimeter with its diameter became an remains until now as some mysterious trick for the human thought.

We have to retain that the perimeter as equal to three time its diameter, is only a recipes that feet well for what it is used.

Case of discrete elemental scale

- universal + conscience + quantum (USA Philadelphia)

- "unicerse" background (USA New York)

There is not a Nothingness in the universe.
Any heavenly body are location determined. Determination are done necessary on concrete reality. Therefore, exinstence in the universe must be done on some background reality. This latter is denoted as the universe breath of elemental matter, the principle of matter concretness reality.

However, I show here that in particular case, a circular measurement can be confused with an elemental discrete rotation. But a dakhion elemental matter displacement is not a circular line while the whole universe space is structured with both circular and linear form.

An ultimate elemental matter can't be concretly represented. However, according to the matter properties it can be logically represented. Therefore, it should be described with the following properties:
1) - It is a two dimensional form built by discrete length.
2) - It has the two basic elemantal motions: rotation and linear ones.

- immutable images (, Austin, Texas, USA)

Immutable elemental matter form
This next figure logically represents an elemental immutable matter denoted here as an object AB.
This figure is composed by elemental length L, the elemental distance of a discrete space. The elemental matter AB is show with continous lines ended by two round as symbol of mass. The length AB is equal to two elemental lengths L. This is a logic of the discrete elemental matter. Because if the length AB is of one elemental length L then there is a contradiction in the discretness of matter. Matter is symmetric that is the two mass points should be symmetric to a center. Thus, if the length AB is of one L then, there is no center because there is nothing least situated between an elemental length L.

AB is necessarily the real logic elemental form of a da-khion.

Now AB should have the possibility of the two basic motions: le linear and the rotation ones. That is one point mass A and B should move in an elemental displacement L. Also, AB should rotate around its center O, but necessarry in elemental angle quantity (a). But because the displacement quantity L is necessarily the one of A and B then, the elemental angle (a) should ne determined by the linear elemental length L.

Finally, the elemental matter dakhion AB is represented on this figure with the basic discretness of matter property. The motion of AB is the trajectory of point A and point B relatively to its center O. We get necessarily a hexagonal figure of its elemental rotation. the rotation is a real one because it is a cyclic angular displacement.

It such case, if we do some approximation we can tell that one cycle can be compared as a circular trajectory. Therefore, in such condition, we can state that the perimeter of such cycle, is really equal to Three Time its diameter! This is the case of a hexagone figure.

This rotation is really a basic rotation. But it can be seen that A and B don't follow a circular line. A and B is displacing along linear polygonal trajectory. Therefore, rationnally it is contradictory to state that "Pi is three time the diameter of a circle".

We must retain that such figure of hexagone may be only choose as symbolic representation but it is not rational to associate it as scientific result.

- center of mass (Thailand)

This is actually the Gold Finger for New Ages.
All my works of the Dakhiometry is underestimated by the current sciences institutions. It's being going all along my life.
So, what have I do to reveal all the deep space understanding of the Dakhiometry to a world that take my Dakhiometry as a joke?
The Dakhiometry have nothing to do with the current Mathematics. It goes deep in the true space knowledge. More than theories, the Dakhiometry knowledge is an efficient science. Determining the gravity center of matter systems is the most wealthy application for human techniques. Knowledge of the center gravity determination is more than to make a great stride for industry. More, it is at least a new stride for human civilisation.
Therfore, what have I to do amongst this inertial Mathematical world, to prove and reprove, to demonstrate things for deaf ears?

- kuwait + law + of + vistuals + and + audio (Kuwait)

There are really vistual audio frequenty when ears are becoming idle for golden agers...

- finite elemente methode calculation center of mass (Germany)

- analytical + method-center + of + gravity (Philippines)

Obviously, Mathematics can do everything with Algebraic formalism.
The problem is that Mathematics ares approximative methods or a precise basic science? Remind that Algebraic appeared because of the Goemetric failure in resolving space.
Note that Algebraic also calculate the very complicate Relativity of "Time and Space". A pure vistual thing.
In brief Algebraic calculation can only give a approximative verification of solid volume. The basic Mathematic problem is: How to rationnally prove surfaces and volumes of any solid. This a not yet resolved issue. Also is the Archimedes' Pi value that is not a rationally proved as mathematic fact, even if this Pi value is quite false but universally and religiously used for a long time in human day life.

- "haw" + km + "squere" + is + Albania (, Greece)

- Exercice+ + déterminer + le + volume + maximal + d'un + cylindre + inscrit + dans + une + demi-sphère (France)

How to inscribe a maximum volume cylinder in a half-sphere? Basic data of a such problem are:

a) - A cyclinder is inscribed in a cube. They have a common vertical axis. With the side of this cube denoted as L. In a circle and in a sphere the aera and the volume of a cylinder is necessarily equal to:
L2; and L3;
b) - Therefore, as a maximum cylinder in inscribed in a cube, The vertical section of this cyclinder is a square inscribed in the half-sphere vertical section.

Solution of haw how to inscribe a maximum cylinder volume in a half-sphere (C):

The construction is reduced to a vertical planar section (C) as shown in this next figure.

Maxi cylinder in 1/2 sphere Solution
The direct solution of this construction is to use the different angles properties in a square. Therefore, the maximum cylinder volume is placed in a half-sphere according to the immutable angle (A) of any square.
Here we have to place angle (A) from the center (O), symmetrically to the vertical axis, of the given half-circle.
this angle intersects the circle at two points (M) and (N). These latter is the diameter of the cylinder base which has the maximum volume in the half-sphere (C).

Maxi Cube in 1/2 sphere - disposition cube sphere (, H-C-M city, Vietnam,

A cube can't be inscribed in a half sphere. This figure shows the construction.
It suffices to use the homothetic of any cube particularly the circumscribed to the sphere (C). This latter side is MN and EF is the diagonal of one the cube face.
In homothetic manner with the sphere center (O) as the homothetic center the inscribed diagonal EF should be on points E' and F'. Then, the side length MN of the cube will be situated at points M' and N' on the sphere.
It can be seen that if the square of side M'N' can be insribed in the sphere circle (C) it is not the case with the cube of side M'N' and its face diagonal E'F. This cube can't be inscribed in the half-sphere of center O.
On the figure, the cube of face side diagonal E'F' but of side M'N' can't be inscribed in the half-sphere (C). On the figure the cube is seen in lateral view to undeline the diagonal length E'F'.

- is + it + possible + to + have + 3 + intersections + between + a + square + and + circle (, Carolina, USA)

It seems that squares and circles association chooses to go from two to two and avoid odd manner of twice being. Because if a square and a rectangle have only three points common with a circle, they will be a simple triangle. And a circle and a triangle is a 180 degrees while a square and a rectangle are a full 360 ones. Really, they are strange things.

- a cylinder inscribed in a cone (USA, Connecticut-Massachusetts-New York State, Hotchkiss Schools)

It is interesting to mention it.
We suppose that all these forms have their axis in vertical position. The proof need only their section along this vertical axis.
We can prove that there is a maximum cylinder volume EFGH exists in a cone one denoted as ABC. These dimensions represent directly their volume. They are triangle and square or rectangle or qadrilateral.

Maxi cylinder in a cone This next figure shows clearly the reasons of this proof.
1) - First we inscribe the cone ABC in a corresponding great cylinder.
2) - Condisering only the planar dimension of these sections, we have the following results:
The triangle aera inscribed in a square is equal to the half of this square one.
The maximum square aera inscibed in a this triangle is equal to the half-surface of this latter.
The ratio between the aera of the triangle and the square inscribed in it is equal to 2
For volumes we have to consider the cubes of these side dimensions.

This proof is valid for any cone and cylinder having a same vertical or inclined axis, but with their base on a same plane. This canonical figure shows how to construct section of a such maximum cylinder in a cone.

A volume of any cone is precisely inscribed between two volumes of a first cylinder where it is inscribed in and a second one of maximum cylinder that is inscribed in it. These two types of forms must have a common axis.

- if + i + leave + the + surface + area + of + cones + in + pi + cam + it + be + marked + as + incorrect (USA)

The Pi as a number is only a number that can be placed anywhere.
The Pi concerning a cone, is not concerning neither its circular base nor for its developed lateral incline aera done in a plane.
In fact the Pi appearing in any circular form is stritly a "circular space constant for transformation". It is not attached as the correspondance between a circle perimeter and its diameter. These considerations are only from the Anciants' empirism where they tempted to associated some corresponding ANALOGY between these two circle data.

- longitudinal axis of a cylinder (Spain, Universidad Politécnica de Valencia)

Naturally, these inscribed forms equalities are valid for any common axis forms and not only for straight axis in square section.

- a + cylinder + is + inscribed + in + a + cone + with + a + height + of + 10 + and + a + base + of + radius + 5. + Find + the + approximate + values + of + r + and + h + for + which + the + volume + of + the + cylinder + is + a + maximum. + Then + give + the + apporximate + maximum + volume. (, Illinois, USA)

The above figure, gives the precise solution. It is there considered aeras. However, these consisderations are valid for volumes calculations.
Let (h) the side BC and r=h/2.
Refering the volume of the cube of side BC the volume of the cone BAC of height (h) and the volume of the cube of side GH, are:
V(cone ABC) = Pi/12).h3
V(cube GHFE) = L3
Where (L) is the side (GH).

According to that:
GH = L = BC/2 = h/2
Then, the volume of the cube of side GH is:
V(cube GH) = h3/8
That give:
L3 = h3/8
Finally the third root of (L3) is:
L = h/2

Because the volume of the cylinder correponding to the cube where it is incribed. It is as:
V(cyclinder GH) = (Pi/4).V(cube GH)

Then, we can consider that the maximum of the cylinder volume is the maximum if the one of its correponding cube GHEF.
It is because a cube or a parallepipede inscribed in the cube of side BC, is maximum in volume if, all its sides are equal to BC where it is fully filling thoughout the volume of its container where it is inscribed.

Therefore, the maximum of the cylinder inscribed in the cone ABC of height and diameter (h), has precisely its heigh and its diameter (L) equal to:
L = h/2

The volume of cone ABC is equal to 8 times the one of the cone GMH, because the cube BC (4.4.4) contains eight cubes GHFE (2.2.2).

Générale formule de fonctions puissances.
Example ici de construction pour la forme du parabole

- diagram schematic de parabolas (Dominican Republic)

In Dakhiometry, movement in space can be classified in an unique spatial formula as:

Any point of motion trajectories can be rationally and precisely described by the summit of isoscele triangle. Its bases is refered by parameters defined by one of its base vertex is tangent to a fixed point. The second base vertex is refered as follow:
1) - For an ellipse, it describes a circle.
2) - For hyperbolas, it describes an arc of circle.
3) - For parabolas, it describes a straight line.

Somme of this formula illustrations are given in the following.
This has a wealthy consequences for describing the matter Condensation Process for heavenly bodies.

- tangent meter (Switzerland csfb)

- draw a circle tangent to a point on a line and another circle (Canada Saint John)

- geometry transformation and construction in a circle (New Zealand, Global-Gateway GGI2)

- how to draw a circle tangent to a line and a circle (Norway, Intility din IT-avdeling)

Construction are done on following reasons:
1) - Center locus (T) of circles (Ci) tangent to a line D and to a point, or a circle C, is a parabola.
Because the general definition of a parabola is as follows: A parabola is the locus of equidistant points from a Centered-Point (C) and a line (D). With a circle defintion as the locus of points equidistant from a center point.
2) - Inversely for a circle:
The locus of any circles (Ci) centers, tangent to a circle (C) is a circle the radius of which is equal to the sum of their two radius.
3) - Locus of centers of any given circle (Ci) tangent to a line (D) is a parallel to the line (D). It is the definition of points parallel to a line (D).

- parabola between two tangents (Fraunhofer-Gesellshaft, Germany)

Some time it is more easyer to determine a parabola trajectory by its tangents.

- dakhiometrie (, Germany)

- draw circle general tangent (Mongolia)

- circle + tangent + to + a + line + and + a + circle (China)

- circle geometry tangent easy learn (USA)

- bisector line point parabola (Italy)

- geometry circle (, Estonia)

Until now Geometry while knowing how to draw a circle with a compass it ignores what is a really a circle. The Geometry realm is only a linear one. It is why this lack in knowledge give rise to irrationnality, the incommensurable space Holes. In Mathematics curves are only simulated by approximative Algebraic tools. Simulation is never a precise definition method. Space is not created and can't be never described only by lines. It is the case for number theory of the Line of Reals number definitions.
Space is not obly Linear but necessarily Linear-And-Circular. More exactly tell with a just order of reasons, basic space is Circular generating Linear structures.
Only with a such basic understanding, human sciences can have a more understanding on behavior of any object in space, the space on Earth and the extraterrestrial space. The Dynamics is only a primary simulation for beginning of a science. The forces is a verry narrow tool for defining movement. Only true relationships according to space structures is the authentic science knowledge of universal laws.
The following figures may appears as usual innocent ones. But really, from there can be deduced precisely the how and the why are the changes in the universe. True knowledge begings on reserach about the absolute space and sciences begin there.

- formule de mathématiques horrible (, Netherlands)

Ce qui montre que vous avez vu que les constructions de paraboles comme ci-après, sont si souples que l'on peut le faire dans tous les sens pour étudier un cas de mouvement donné. Alors que la Géométrie Analytique est figée raide, dans ses formalismes qui ne permet pas de s'adapter aux cas réels des études.

- geométrie pour les petit, circle (, Chile)

- circles geometry (, St Teresa's Academy, Kansas City, Missouri, USA)

- geometrija krog (, Slovania)

- tangency constructions (University of Belgrade, Bulgaria)

- "cricle" plane geometry (, Vietnam)

- ancient geometry circle trace (China)

- how to analyze sacred architecture with geometry (USA)

- interesting composition of rectangles and circles showing divergence from a converging point (Pakistan)

- geometrija (Croatia) - Vietnam basketball (, Vietnam)

- fruit de vietnam (China,

- ICI PAINT for car in Pakistan (Pakistan)


- Vietnam fruit (Vietnam,

- parabole + et + circle (Vietnam)

Circle tangent to Circle and line
Therefore, the construction of any circle (Ci) tangent to a circle (C) and to a line (D) at point P, is given on this next figure.

Function general form:
The Algebraic formula
can also be extended directly as
when y=x

and more generaly, when (Y) is any quantity form one usually writes it under so many algebraic number formalisms. Example given as root or exponetial forms...
However, this is here a more generalized view point through spatial figure forms. The usual geometric or algebraic parabola is nothing than a very particular understanding of a more complete spatial structure.
In Dakhiometry, a parabola is nothing else than a whole spatial complex description. For example, in spatial language, a parabola relationship can represent an aera of a square! It is a new understanding of the Potential law of matter in space. With basic understanding of matter there is an unique science of matter. There is no dichotomy between pure Ppatial Language and Physics.

Therefore, we have there the precise general formula of spatial constructions for all power functions where are included the parabola, hyperbola and exponent forms.
All these functions rest on an unique basic second degree parabola form construction.

A parabola is a form belonging to the space structure. Consequently, exponent functions are also space structure. The Algebraic forms are only imperfect and approximations understanding of space when using Numbers of conventional language.

- parabolas joke (, Waterloo Region District School Board, Kitchener, Ontario, Canada)

- if + friction + be + neglected + what + is + the + characteristics + of + the + motion + of + a + heavy + object + thrown + violently + downward + from + a + tall + building (Philippines)

Throwing any object is to communicate to it a speed for an uniform motion. So for this given above case it is usually written the parabolic falling motion as follows:
      y = V0 + at2
y      is the object falling trajectory
V0;   is the initial throwing speed
a;     is the instantaneous potential of the object location
t;     is the duration of the trajectoty from the starting point.

This is the usual algebraic mode of analytic geometry.
But according to the Dakhiometry's spatial language, this phenomena can be easily constructed and directly measured precisely any point of this trajectory. More this spatial construction can be applied in any case of a given situation and in any scale of the figure.
Examples of this Dakhiometry language is done in this web site about the Foucault-Pendulum false so-called law.

Important Notes
If you are asking for such known problem, may be it is because you want to know how is my answer about the "gravity" provide that the classical known gravity is the Newton's central force one.
The parameter (a) here, is the location potential of a system that have a Rest-point because, a Constant gravity as the (g) is false as general factor. The (g), e.g. as 9.8, is false because the Newton's Universal Gravitation is only a false empirical hypothesis.
The true universal law of space is that any celestial system is basically the space duo parameters Potential/Rest-point.
Therefore, in such system, the gravity factor denoted here as (a), should be an accelerated gravity factor of object falling motion toward the Rest-Point. This is because the trajectory distance is the square root of potential energy.
Remind that the Newton's central force is inversely proprtional to the squared distance denoted as function of (1/R2). So, the usual use of Earth gravity as (g=9.81) is only an approximation for cases of Earth surface objects. But this central force theory implies that the pressure in the Earth center is very high. While with the Potential/Rest there is no such contradiction. A rest point for an object means its equilibrium situation. Therefore, near the rest point there is two cases of equilibrium:

1) - Or the object has no more internal kinetic energy then it stand at Rest. All of its initial potential energy was transfered to the other surounding matter
2) - Or during the formation state of interactions, this sobject cannot lose all of its initial potential energy, then the amount of this energy is distributed as kinetic energy in such manner that this object will be orbiting aroung the Rest-point.

We have there, the shematic of the Dakhiometry matter condensation process law when stars is forming in their globe structure.

Therefore, in the case of the universal Space Potential/Rest law, the Newton's Central Force is irrelevent to describe celestial bodies as how they are formed and why a star and a galaxy systems can appear as universal orbiting systems.
It is clear that the Newton's Central Force is not only a quite simplistic but also a false model.

New simple and rational Spatial definitions and constructions of Conic

- how to construct a circle to touch another circle externally and a given point (United Arab Emirates)

You may have your own solution. Here is an another one proposed.

General Basic principle
Any spatial structure can be defined and genrerated from circle. The basic one is the squaring a circle. From there comes first the squaring an ellipse.
Example is given here for hyperbola figures with circle (Co) as line director.

Circle tangent to Circle and pointYou may have your own solution. Here is an another one proposed.

The construction uses the radius (R) of any given circle (C) that have to be tangent to circle (Co) and the point (P).

These constructions are nice generators of hyperbola from all the locus of (C) centers. Axis (x;y) of these hyperbola are determined by the middle of tangents from (P) to the fixe circle (Co). OP is the bisector symmetrical axis of (x;y) angle. The middle of OP is the axis intersection. It is clear that axis (x;y) are limits of these hyperbola. These locus are really hyperbola because it is clear that these axis are their limits as asymptotes. While a parabola can't have any asymptote.

- using tangent to draw conic section (, University of Manitoba, Canada)

Term Conic is originated from the formalism of solid cone sections. Conics are then attached to these formalisms.
Howeve it is more wealthy to undestand that locus points of conics are locations of a particular space structure for object displacements. Then a tangent has the meaning of symmetry for the energies sources of these displacements.

- a circle and its tangent which show the properties at the point of tangency. (Carolina, USA)

Actually. From (P), it means here an asymptotic property of variables.

- como se hace un plato de parabola (Dominican Republic)

- easy + dependent + vaiable + picture (, USA)

- hyperbola stream function (, USA)

- hyperbola edge graph (Hong Kong)

- The Analysis of Beauty conics (, Pennsylvania, USA)

- An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry (, USA)

- conic graph arts (, California, USA)

- tangents to hyperbola (, Australia)

- An introductory account of certain modern ideas and methods in plane analytical geometry (Australia)

- conic drawing of Apple logo (, ELA Group, Inc-Pennsylvania LANDSCAPE ARCHITECS, USA)

- reciprocation of a circle to draw hyperbola ( (Hsinchu City Education Department, Hisinchu City, Taiwan)

- architecture hyperbol (, HoChiMinh city, Vietnam)

- trisection hyperbola (Korea)

- Sydney + opera + house + hyperbolic + integration + calculus (Australia)

- hyperbolic paraboloid apply real life (Vietnam)

- hyperbole math première résolution (Ecuador)

- what is "tha" relationship between parabola and hyperbolas (USA)

On these basis of isoscele triangle, deduction can unfold more wealthy cases as liberty of large understanding about these elemental space structure for movement. What can never be known by the usual conics of the Analytic geometry.


This figure show how we can get the orthogonal axis hyperbola when tangent from point P to (Co) form a rigth angle. The whole hyperbola is generated by symmetry on the bisector axis for (Co) and P positions.

New main hyperbola characteristics are:
1) - Circle (Co) is the circular Line director. (Co) is a more precise basic parameter for hyperbola then defining it as "any hyperbola point as a constant difference between two fixe focus points"
2) - Pont (P) and (O) are the focus of each hyperbola branch. The one is the director center of the other.
3) - (T) is the tangent of any hyperbola point defined as the bisector of angle {oTp}

Conical belong wholy to rational and precise space structure. The consequences are of great fertility.

- how to construct a hyperbole (, so California, USA)

Practical applications using simple tangent constructions

- greatest constructions (Bulgaria)

For example, this next figure can be a collector at the focal (F), of the surrounding electromagnetic and sound energy in a solid angle. An another practical application is to use the hypebolic surface to produce dimmed headlight of cars.

- ellipse AND maths AND headlight (Sri Lanka)

- greatest constructions (, Mexico)


- How to use mathematies (Cambodia)

- solid angle satellite (Netherlands)

- real math hyperbola (, Victoria, Australia)

It is interesting to use a hyperbola surface to focus by reflexion all the electromagnetic of space in a whole solid angle. The simple spatial hyperbola defined here is useful to adjust the hyperbola parameters for construction of a choosen solid angle. It can be in 3D symmetrical to one central axis (OF).
May be, a hyperbola is more interesting to concentrate for diffusing or receiving not directional electromagnetic radius energy.
Emission of sound by a loud-speaker is there less directional and more realistic - HiFi - than as for a spherical or parabolic speaker.

- headlight hyperbola (, USA)

With the squaring circle law the unit solid angle denoted as (sr) steradian, can be precisely defined as a circle of a sphere instead of refering to a square surface. On this figure the solid angle is the one with center (O) of sphere (Co).

- assimetrical speaker dispersion (, Spain)

- multiple hyperbolic paraboloid, architecture (, Texas A&M University, USA)

Possibility of conics sparial constructions is very useful for architecs. These latter are also engineer but they need artist form feeling for designing environment interaction of city and individual living. Therefore, it is more natural for them to manipulate forms from direct drawing of projects. Computer can complete at final state for producing practical dimensions of construction structures. But drawing spatial forms is the direct contact for ergonomics in conception and design between artist and engineer .

- parabolic solar cooker plans (, Mexico)

Kowing how to determine any tangent of a conics is useful for determining electromagnetic ray reflection of a given conic surface.
Using parabola for Sun rays concerns only the direct Sun ray onto the parabola surface. A parabola use only parallel Sun rays. It is more interesting to collect non parallel rays in a whole solid angle because Sun energy comes also from the whole atmosphere. Thus, an association of a central parabola with a peripheral hyperbola surfaces can be precisely determined by spatial construction for a maximal Solar energy collector. This may be for an individual solar cooker as well as for a biger installation.

Important practical notes
We are used with computer that can give any analytical conics form. It is why these present spatial constructions of conics seems to be only curious things. However, the importance of the present spatial constructions should be understood as:
1) - Spatial constructions of conics curves are rational precise and continous locus of points.
2) - The most importance of its properties is found in practice. Because spatial method allows the mastering of conics curves. For examples, a parabola or hyperbola can be defined anywhere in a given structure, between two given points. Then, it can be adjusted with factors from that we can match its curve to the given structure. In architecture, one need only a conics form to become harmoniously integrated with the other system form. In brief these spatial methods of conics can be easily manipulated with suppleness and are no more only primary forms produced by machines.

Complication and Error about Analytical Mathematics on Conic definitions

- géométrie analytique joke (Canada)

- arabolic + hyperbola + boy + scouts (Luxembourg)

May be.

The so-called Conic is from the Anciant's empirism the thinking mode is to Things and then to "analogically think" their everyday observations.

What is "conic?

One nows that Conic is originated from curiosity seen according to the different Figures of light shadowed on this cone.

As light is linear then, the Conic are from Linear Figures. Whatever are the algebraic function formalism and the semingly "curves" of these conic functions,

It is why Conic Function espressed by X/Y, also by X/Y/Y or more higher dimensions of lines system reference, these conic ares strictly of Linear Functions.

What is then a NOT-LINEAR function?
The Not-Linear function is simply the Curvilinear one.

Most of mathematicians ignore what is this curious thing as "Curvilinear Funstion"?

Therefore, I am sorry to tell them that all of the "conic" given in this present text are precisely from Curvilinear constrution ones!

Any of the current Conic described in the current Mathematics have to be thrown avay.
All of any functions is NECESSARY defined by CIRCLES!

Therefore, any of the current "Conic" defined by algebraic method are not the exact expression. Their utility is nothing else than to "prove the Infinity or the Nothingness ideology"

There is ONE basic universe Circular Function that shows the property of the universe Circle not as the endless Infinity/Nothingness but as the Permanence of a Circle. The Perimeter of a circle is not the infinity of Beginning and the Infinity of its Endless as was stated by Moebius. The truth is that the perimeterr of a circle is the symbol of the Permanence.

However, the perimeter is not the correct expression to express the Permanence. Because the Permanence should be described by the Isotropic property of the universe Space. Because the Circle is the characteristic of the Space Direction while the Distance is the Linear characteristic.

Mathematicians with their simplistic empirical Mathematics come up against a barrier of uncomprehension when they have to define the Angle as long as they ignore what is the difference between the Circular and the Linear space. It is why with Mathematics and their Trogonometry they will NEVER resolve the Trisection of an Angle.

Precisely, to resolve not only a trisection but to resolve the Angle Division they should at first resolve their "Circular Conic", the Conic that has no Beginning and no End but rationally and wholy constructed. Simply tell, the Dakhiometry had resolved this Universe UNIQUE Circular Conic!

It is not usefull to expressed that the Dakhiometry can defined this Unique Circular "Conic"... and then shows rationelly what is the Trisection or the divison of an Angle.

In Mathematics parabola ellipse and hyperbola are define as;
Conic as generated by A POINT AND A LINE. And written as:

M(x,y), ax2 + by2 + dx + cy + f = 0

It is a great error and a confused false definition.
Here above was seen what is a parabola and a hyperbola according to the Dakhiometry. The Analytical Mathematics for conic is proved as contradiction according to the definition of what is an asymptote.
Because if conic is generated by a focus and a line it is only an artificial process. The reason is given in the following:

Definition of an asymptote
Let a function y = f(x)          (f-1),
1) - (f-1) has no asymptote if (x) and (y) are simultaneously unlimited quantities.
2) - (f-1) has an asymptote if only (y) goes toward zero when (x) goes to unlimited quantities and inversely.

a) - A parabola is generated by a line director and a focus point or a central point. Then a parabola has no asymptote because a distance from a point to a line has no limit.
b) - A hyperbola is generated by a circle and a focus point. Then, the tangent to this circle from the focus point has a limited possibility. This limit is the condition of asymptotic situation for hyperbolic function.
c) - Perimeters of an ellipse and the one of a circle are cyclic and have no linear infinity. Therefore, generation of an ellipse is limited and has no unlimited variation and no asymptotic conditions.

Therefore, analytical Mathematics defining conic as generated by a line director and a fixe point, state that there is no possible asymptote for hyperbola. While it is valid for parabola and strangely, for ellipses.

This error is originated from Anciants studies on conic that had a partial view on parabola and in continuation for modern Mathematics. We see there that the line plus a point for conic are artificial Mathematic definition.

The present parabola and hyperbola exposed above in this text are really a parabola an a hyperbola precisely and rationally defined according to spatial language..

Les ellipses comme coniques

En l'espace on peut faire la moisson de joyaux que sont ses structures, lorsque l'on sait les révéler. Les structures de l'espace sont les racines par lesquelles toute lois universelles se manifeste. Une structure rationnellement definie est une lumière permettant de comprendre les milles et un phénomènes du monde.
Par exemple, une mono cellule est centrée autour d'un noyau. Que fait-elle pour de multiplier? Elle dédouble son noyau, on le sait.
Ainsi, dans l'espace il existe une structure raison de base du dédoublement d'un cercle d'où apparaît la forme d'une ellipse. Ce n'est seulement par le langage de l'espace que l'on peut voir et comprendre un tel joyau de raison. Depuis des millénaires, quel mathématicien peut prétendre le voir à travers ses sciences de l'ellipse comme conique, péniblement décrite par des formules abscons et approximatives de la géométrie analytique? D'autant que les Mathématiques sont pour eux que les manifestations d'un Esprit qui n'existe pas, ici-bas, mais qu'ils croient que leurs corps ne sont que des pantins manipulé par lui. On peut en rire, si ce n'était qu'une mauvaise plaisanterie mais l'abrutissement de l'homme par de telle idéologie ne peut descendre plus bas. Plus con que ça, tu meurs.

Il me faut un effort pour me decider à vous révéler le conique ellipse. Lorsque je vous présente ce qu'est l'ellipse comme conique, le plus libre d'entre-vous verront que les Mathématiques sont d'autant compliquées qu'elle est nulles. Il n'y a pas de Mathématiques, cette science dure. Il n'y a que des mathématiciens rigidifiés, pauvre en réflexion, prompt à imiter les perroquets et robots.
L'équation générale des coniques, cité ci-dessus, reconnue et adulée par tous, en milieu scolaire institutionnel, attribuée à Descartes et autres des temps contenporains, n'est que bricolage sur les conique, qui ne dit rien si c'est que plus c'est compliquée, plus les Maths sont forts. Cette tare est transmissible par contagion pour le formatage des esprits des générations et générations de scolastiques.

L'ellipse comme conique selon le langage de l'espace est d'un signification vaste et étendue, particuluèrement pour les mouvement explixitant les situaions des astres et le processus de la Condensation de la matière, selon les lois de l'espace comme Potentiel. Quelle sont ces sciences qui ne sont que toute fauses de la tête aux ongles des orteils, en math, astronomie, physique et science de la Terre?

Par expérience vécues, je sais que tout ce monde dit de science est sourd aveugle et muet du penser.
Je vous laisse, essayer de sortir de vos coniques maladroits et fausses, servant depuis des siècles à racconter des bobards sur la mécanique céleste et qui continue encore malgré les résultats que je présente en public sur Internet, depuis déjà 12 ans!

Allez, réjouissez de vos sciences infantiles et ne vous étonnez pas que le Terre souffre de sa maladie imaginaire telle que l'Effet de Serre et de son Enfer sous terre.
Au lieu des vos Pis folkloriques selon d'Archimède, faites la quadrature de l'ellipse. La Constante de l'Espace qui vous a été grâcieusement présentée, ne vous a servi à rien.

Conclusion sur les coniques

- la + solution + et + l'unicite + des + équation + de + la + forme + parabolique (United Arab Emirates)

Vous aves là, la vue d'un regard se tenant à partir du centre du problème.
En effet la racine des raisons des lois universelles est réellement le cercle comme concept logique, d'où radiusonnent les raisons d'un espace parfaitement défini de l'univers où tout n'est que solution et où il n'existe ni problème du passé ni incertitude de l'avenir. Ce n'est pas là des paroles de projections idéologiques d'homme. Ce n'est que le rationnel des Faits de l'Espace des lois universelles.


Enoncé de la Dakhiométrie: Les coniques sont pratiquement, deux sommets fixés et déterminés, d'un triangle isocèle PFH, forment un système de référence et de symétrie pour tout point de l'espace univers.

Dans le cas des figures classées comme conique, elles sont des variations d'une même raisons de base. Ses aspects ne sont pas des dispersions de similitudes que l'on a mis dans un même sac par analogie formaliste. Elles sont bien l'unicité dans sa diversité. Le voir ainsi appartient au domaine de la connaissance alors que ses applications sont des qualités de science exacte.
La figure ci-contre, indique la définition pratique commune de tout conique. Elle se fait par le triangle isocèle PFH. P est un point d'une conique dont F est le focal et H un point de sa directrice. Il n'est représenté ici que la parabole et l'hyperbole. L'ellipse n'y est pas indiqué puisqu'il n'est pas encore explicité ici. Mais l'ellipse fait partie de cette définition commune.
Tout l'espace de l'univers, peut être décrit par la forme de conique. L'univers est un cercle et du cercle peuvent s'exprimer pour la Condensation de la matière en astres qui se fait selon la dégénérescence du cercle vers l'ellipse. Cette transformation est l'expression du Potentiel de l'Espace en énergie cinétiique. L'Astronomie est intéressée par la description des formes coniques. L'ellipse concerne la formation des systèmes astraux. Puis, en interne seulement aux systèmes astraux, peuvent s'appliquer le parabole et l'hyperbole.

La description d'une géométrie Non-Euclidienne par des espace courbe n'est qu'une théorie fausse parce que née d'idéologie construite par génératio d'imageries de l'homme. Il est faux de croire que l'espace est un plan hyperbolique courbe, parce que les lois universelles ne s'exprime uniquement que dans un plan. Dans le cas de l'espace comme plans courbés, nous avons l'expression de la preuve de l'ignorance des mathématiciens et physiciens d'une ignorance de l'Espace qui n'est que leur contradiction d'un Néant. Néant dans lequel, oui selon la science officielle il y a des places dans le Néant, chacun y place où il veut Sa théorie personnelle qui l'arrange. Sacrés savants! Ceci dit, vous seriez dans le faux de conclure par là, que la Géométrie Euclidienne est la bonne. Cette dernière n'est qu'une approche lointaine de l'Espace par empirisme maladroit et que de toutes les générations de mathématiques, aucun ne sait définir rationnellement l'espace si ce n'est que par le témoignage de leurs dessins.

Voici ce que la Dakhiométrie donne.

1) - Expression de la connaissance:
Après la transformation du Cercle en carré qui est génération des Directions en Distance, la mesure de l'espace peuvent se faire par dégénérescence du cercle en expression selon les lois de coniques. La dégénérescence du cercle se fait par dissociation du point centrale, qui ne peut s'exprimer qu'en Direction, en deux points séparés marquant de la Distance.
2) - Expression de science de mesure:
Tout l'espace de l'univers peut alors se décrire à partir de deux sommets référencés d'un triangle isocèle, pout pour définir le troisième sommet dans la totalité de l'espace univers. C'est là la vraie expression des coniques.

Alors que les Mathématiques restent figées depuis des millénaires, sur quelques spécificités des formes de paraboles, d'hyperbole et d'ellipse, on peut constater la connaissance pleine de l'espace en Dakhiométrie. Ainsi, sur la figure, on peut voir que dans le triangle isocèle PFH, si l'on se réfère aux deux points F et H, on trouve dans l'espace les formes de parabole, d'hyperbole et d'ellipse, décrivant par le troisième point P. Mais que si l'on se réfère aux deux points {P, F} ou {P, H}, on trouve la forme-source qui est celle d'un cercle. En variant les paramètres du triangle PFH, on peut ainsi décrire toutes les variances de point de la totalité de l'espace. C'est bien le cercle qui est la Source de toute forme de l'espace. Ceci n'est que la réciproque. Parce qu'avec l'ellipse on trouve la preuve du théorème directe où, d'un cercle, il naît une ellipse et les autres formes de base de coniques. Voilà la science vraie des lois de l'espace où il n'y a pas de dichotomie fantaisiste, un mauvais mirage entre "Mathématiques et la Physique" ou Esprit-Matière.

Voilà en bref, le nectar des raisons qui fait la rationnalité humaine. Il ne s'agit pas de croire ou de ne pas croire à mes exposés. Il n'est que la nécessité d'être humain.

L'inertie des savants institutionnels s'accrochant à leur besace de Trucs et Astuces de croyance, est terriblement fautive dans le reniement de la raison humaine. Leur inertie s'exerce à étouffer la Dakhiométrie, la seule et unique chance pour l'humain de devenir adulte.

- what + is + the + meanning + of + "pout" (, USA)
Sorry. "Pout" would hopes to tel for POUR or FOR. "Pout" is no more the impudent vocabulary of heretical fingers that are worying with the usual everyday inhospitable keyboard.

- loie + de + la + gravitation (Estvideo numericable,, Alsace)

C'est au féminin il faut donc mettre le mot loi au féminin.
Alors, la loi loie de la Gravitation a été l'aboutissement, d'une recherche désespérée qui avait été le tracas de toute une longue époque où l'on ne sait pas pourquoi tous les dignités tombent par terre, lorsqu'elles trébuchent.
Ayant réussit à façonner une définition du mouvement, appelé Force, Newton y prenait appui et pensait à l'association "évidente" de la masse et du mouvement. Il peut donc dire qu'il y a mouvement, lorsqu'il y a une Force. C'est ce qu'il désignait comme Vitesse ou variation de vitesse puisque lorsqu'il y a un mouvement, il y a aussi, des mouvements-dans-le-mouvement. C'est ce que Leibniz appelait la relativité. Justement, par la Force, Newton ne défini pas vraiment le Mouvement car la Force n'est valide que par le mouvement-du-mouvement, une "accélération". C'est pourquoi, en utilisant les lois de Newton, la Mécanique a un mal fou de s'acherner à définir le mouvement, prenant soin de faire des acrobaties terribles de notations formelles pour justifier l'écriture d'une force, en définissant chaque mouvement d'abord par sa référence. Sans ces précautions, la Force ne dit rien du tout sur le mouvement. C'est pourquoi, Einstein doit écrire sa formule magique:

* non pas seulement par : E=mc2
* mais par: E=(mv2)i + mc2
qui veut dire que le mouvement est relatif à un mouvement initial de "je n'en sais foutre rien". Hors de la dévotion, vous constateriez que la vitesse limite obligatoire de ses photons, n'est que de la connerie attrape-nigauds. C'est exactement, ce que cette formule vous dit. parce qu'il faut y ajouter une vitesse que l'on ne sait pas mesurer avec quoi? Mais voyons, avec la science de la Force de Newtion!

Il reste à "trouver une raison", ce que l'on peut dire plus justement une justification ou mieux, "se faire une raison" pour la masse. En conséquence, comme la légende de la pomme-qui-tombe le dit, elle tombe bien sur Terre et non sur la Lune. Oreu, comme la Lune est évidemment plus petite que la Terre, on peut en faire-une-raison, consitant à associer la Masse comme la Source de mouvement. Dans ce cas, la Terre plus grosse que la Lune, mange donc la pomme. D'où la Loie de la Gravitation est toute "fondée" selon le témoignage massif ou unanime de tous, que la Terre et plus grasse que la Lune, d'abord parce qu'elle donne des fruits et qu'ils y pleuvaient à gogo.
C'est ainsi que se passe la plus part des recherches scientifiques, fondamentales ou appliquées. C'est vraiment l'empirisme de l'Art de Se Faire une Raison.
La preuve, La Relativité a une raison toute trouvée dans la Loie de la Gravitation Universelle de la Dynamique newtonnienne pour édifier l'édifiante théorie des Champs. Lorsque l'on est d'accord pour mettre au plus Haut, la valeur Sa Croyance Civilisatrice, qui évidemment, est toujours la plus Haute, la plus Grande, la dévotion nous tire par le bout du nez, pour "prouver" que, oui, la Masse du Soleil, dévie bien les "photons". C'est juré, craché. Vous êtes incrédule? Vous en recevrez le crachat à la figure, pour vous placer an asile, parce qu'en ces temps modernes, on n'évite de parler crûment, de la cuisson au bûcher...
Ceci dit, on ne critiquerait seulement que si l'on pouvait trouver d'autre véritable raison de la nature, pour cette pomme qui tombe toujours de son pommier.
a) - La pomme tombe parce qu'elle va se pourrir. C'est un témoignage béton. Pourtant, aucun scientifique n'en a fait une théorie... Détrompez-vous. La Croyance est aussi une science qui ne porte pas la même robe. La pourriture est toute une philosophie sur le vie et la mort, son destin. Evidemment, elle n'a pas la robe que porte le BigBang et le Big Crunch, tous deux, sont issus d'un Big Trou Noir, scientifié.
b) - Il reste une chance. Celle de savoir ouvrir les yeux pour se rendre compte qu'en réalité, la science en cours, passe son temps à courir derrière son ombre. Elle jure tout le temps par l'espace mais jamais, ne se rend compte qu'elle parle d'un absent qui est de taille. Vous remarquez l'association "Absence de Taille" ou mathématiquement "la Grandeur de la quantité Zéro" ou mieux enocre, "l'Immensité ou l'Infini du Néant".
c) - Finalement et en bref, il n'y a de science rationnelle que par l'éclairage de l'Espace Matière, un Fait de l'univers si gros, que nul intelligence ne daigne regarder. L'énoncé de la loi spatiale est simple: Tout objet est défini dans l'espace par son point de repos. Cette définition se fait par le phénomène Mouvement.

La voici:
1) - Il n'y a pas de mouvement absolu de l'objet, lorsque l'objet est au point de repos.
2) - Il est en equilibre-par-le-mouvement, lorsqu'il n'est pas en son point de repos.
3) - C'est ainsi qu'apparaît le phénomène Energy qui n'est que l'expression de l'espace comme l'Energie Potentielle

Prenez soin de lire ces définitions de la Dakhiométrie. Car, il s'agit précisément de MOUVEMENT ABSOLU. Alors voici non pas l'explication par l'art du discours mais, la raison qui explique que si l'on tombe par terre, c'est que tout objet en surface de la Terre et à sept lieux du centre de la Terre, le point de repos commun de tout l'astre Terre... et non des objets de la Lune et d'ailleurs.
Evidemment, si l'on tombe et que la loi dit que vous êtes en équilibre... Cependant, c'est là la difficulté des sciences du Témoignage de comprendre que l'on tombe pour le plaiisr des lois et qu'il préfère accepter de subir la justice d'une poigne de fer d'une Force qui vous y oblige.
Mais, ce n'est pas ici, une autre évidence de témoignage. Une construction de la structure immuable de l'espace peut se démontrer par la transformation en énergie d'un point à une distance de son point de repos.
Je le répète encore:
Le Potentiel propriété de l'espace, définit la Mouvement absolu. C'est-à-dire, le mouvement en soi. C'est pourquoi, il n'y a que l'énergie de vraie, pour décrire exactement le mouvement. Voilà ce qu'avec l'habitude de déduire, on peut faire avec le fait de l'espace comme Contenant et Contenu.

Proof of rational Circle into ellipse transformation.
A most basic transformation
as physical meaning after the squaring a circle

- Integration in 3d sphere and isosceles triangle (, California, USA)

- exponential curve vs tangent curves (3Dexamples of internally tangent circles in real life, Washington, USA)

- construction in the circle (, Bahamas)

- Jordan University of Science and Technology Doctors (, Jordan)

To complete the spatial system of the Dakhiometry's conic figure, here is the proof of the rational generation from a circle of any ellipse in space.

- how to "drown" an ellipse (, Manchester, UK)

- how to construct ellipse my choosing points in a rectangle (USA)

Actually. It can be construted any ellipse inscribed in a given rectangle with this next construction principle. Then with the four point on the four sides middles, the circle (C) is determined to construct the seeking ellipse.

- billard + en + forme + d'ellipse, + tirer + foyer + sur + le + rebord + sur + foyer (, Université de Lausanne, Switzerland)

La qualité des joueurs de billard est d'avoir l'esprit géomètre très aigue. On le voit se manifester à coup sûr, par les champions qui voit l'espace du billard non de manière analytique mais, cet espace dans son entier complet, où il n'y a plus de passé ni de futur. C'est ça, l'espace.
Alors, avec un billard bien au point en forme d'ellipse, je crois que les joueurs s'en régaleraient à y concevoir leurs coups magiques avec précision. Parce que l'espace d'une ellipse est très bien plus riche en relations spatiales que celles d'un rectangle.

- how do I teach ellipse by material (Turkey)

- ellipse in real life (Vietnam,


Because universe space is pure absolute structure. Therefore, matter should be constructed according to self portant structure. It is why archtectural estetic can found construction founding on natural function logic without which geometrical forms are only coagulated sceneries.

- earth + rotation + basics (

An ellipse is from circle family.

A star orbit or any object in space is generally composed by two energy components:

1) - A first enery type is the iso-potential circle relatively to a Zero point energy of the system.

2) - A second energy type is the kynetic energy for rotation in the perfect iso-potential circle around the Zero Center energy.

Both of these energy types are refered to its Zero Center constitute the universal Location factors of any object in the universe Spece.

In practice most of stars orbits are done as elleptic ones but not as a perfect circle.
It is because they are not precicely done on a given iso-potential circle. It is because stars are form from the Matter Condensation Process where the energy distributions are not done by discrete manner from the initial elemental matter cloud. Therefore a star is composed of:

EP + ER + Edelta(R)

The Edelta(R), is a delta-(rotation kinetic energy) is a cyclic variation of the star rotation orbit.

The effect of this later is to pulse the star in an elliptic trajectory. This latter is no more than a cyclic rotation energy done around a given average circular iso-potential orbit.

The differential rotation orbit around a given average iso-potential orbit is expressed in Spatial Language of the Dakhiometry as shown in this next folowing basic construction of an ellipse.

The circle (C) of this system defines the characteristic of the initial personal cloud from where the star was formed from a larger star system. For example Matter-condensation produces the Galaxy, Star series, Star systems and Planet systems.

One can note that in space everything is basicaly from a circle, not only for the Square but particularly also for the Elipse forms.

According to the circle (C) one may note that it is wrong to tell as by Kepler did it that an orbital ellipse has TWO FOCUS.
The truth is that an ellipse should be defined from a centered structure defined by a Circles (C). It is a general property from the Dakhiometry that allows to define all the ellipse spatial form properties as aera and volume of ellipsoides

One can note on this next figure that the ellipse (MN) form is produced by two circles (C1) and (C2) rotating on the main circle (C). The two ellipse focus is only a secondary property consequuences!


- architecture turkey (Vietnam,

- architecture, jardins, ellipses-architecture, jardins, ellipses (Velizy, France)

Avec la possibilité de manipuler les courbes dites côniques montrées ici, on peut ajouter les formes parabole-hyperbole-ellispse à l'architecture en générale. On peut envisager les projets de formes sur le plan du terrain et y placer les courbes voulues. Courbes qui peuvent être maniées facilement comme on le voit ici. Ensuite il suffit de les reporter en longueurs déterminées sur le terrain.
Vous aurez intoduit par là, les caractéristiques esthétiques modernes dans l'environnement urbanistique. La peinture cubiste a été bien insolite dans les moeurs des formes rectilignes et trompe-l'oeils. L'architecture ne doit plus servir à écrire des messages linguistiques ou des symboles d'intentions anthropomorphiques d'ambition démesurées des divinités qu'ils soient Profanes ou Divins. Elle n'en ferait plus que son enterrement en érigeant sa propre pierre tombale baroque. Nul ne veut plus la lire ni la vivre parce que l'informatique s'en charge pour tout ce qui est de discours à profusions.
L'architecture se doit d'être ce qu'elle devrait être : les justes mouvements vécus de l'homme. Ce en quoi à côté desquelles sont restés emprisonnés les architectes, fautes de moyens pratiques offerts par l'enseignement des Mathématiques. Pourquoi rester dans la ligne d'Euclide, la pyramidal symbolique, ou le cube des formes? Est-ce parce que l'on ne sait pas doubler un cube sans mentir? Il était temps de libérer un peu plus les formes dans le paysage de vie pour briser la rigidité des mentalités de ce monde. Monde qui voudrait avancer et qui donc est resté encore en retrait, toujours endormi dans le Linéaire des Millénaires obscurs.

L'intelligence spatiale est plus que le bond en avant de la pensée humaine. Ce serait un crime contre l'humanité que de chercher à l'étouffer et le renier par le conservatisme nombriliste des scientifiques et des responsables en cours.

Il me semble que seul l'architecture peut l'intégrer dans le vécu et avec une meilleure efficacité, dans la mentalité du monde en cours. Si l'on examine l'histoire de l'architecture moderne, quoique se tenant en arrière du discours, l'architecture urbaine a un rôle première dans l'évolution des mentalités. Pour le voir, allez dans les quartiers de styles architecturals différents de votre ville. Vous y verrez ces différences détonnantes de mentalités de leurs habitants.
Les architectes osent exprimer par la liberté de leurs oeuvres centrés sur l'être humain, là où les formes intitutionnelles anciennes dans ses virtualités, le répriment dans son conservatisme. Que nous dit le nid d'oiseau, si ce n'est que pour mener les oisillons vers leur vie? C'est pourquoi le nid d'oiseau parle de l'universel. Ainsi l'architecture se doit de s'orienter sur l'universel de l'homme et non de ses idéologies qui en sont les contraires.

- transmutation + circle (, Japan)

Actually. A circle can be transmuted or transformed into different forms. For example, on the above figure case, the circle (C) can be transmuted into the line segment (yN) or any ellipse of axis (yN) or into the circle of diameter (yN). There are also other basic transformations else than these denoted figures. Only with more knowledge on the space properties and when familar to spatial constructions one can get many astonishing and deeply useful results.
The physical meaning is that le segment (yN) is the trajectory of a free falling body, the ellipse is an mixted motion resulting from rotation and falling motion components. The circle of diameter (yN) is only an homothetic motion. More natural motion form can be deduced from there.

- transmutation circle sides (, Iowa State University of Science and Technology, USA)

The matter condensation process is really a transmutation of Potential into kinetic energy. This figure is siggnification of its rational definition. The plane disk (C) is the surface of potential where the original elemental matter can occupy in a plane surface. The condensation process is to reduce this pure potential in reducing this surface to produce motion of a final system. This planar law happens in any space direction so that it happens in 3Dimensions.
a) - Condensing matter in the center of (C) is impossible according to many basic principles as discretness, identity, conservation of space matter,... ect.
b) - Then, only reducing matter space occupation can be done. The concerning quantity is the aera. Transforming (C) aera in energy is then transforming length dimension of (C) as the square root of aera.
c) - The perfect transformation of (C) give then a perfect another circle with the half (C) diameter. But this case is only a particular possibility in the condensation process liberty. Therefore, there is also same dimension transformations but in elliptic forms. These wealthy final condensation forms can be observed in Astronomy. The Earth orbit is precisely a just elliptic form that can generate Earth internal energy variation in such manner that complexe life can be developped and maintained.

Pure space locations transforming into kinetic energy for construction of wealthy in life can be denoted as transmutation by universal laws.

- spherical astronomy

- examples of internally tangent circles in real life (, Minnesota, USA)

- real life internal tangent circles (, USA)

From a circle (C) and any point (F1) of any of its radius and from (C) center (F2), an isoscele triangle (F1PE) defines a point (P) of an unique ellipse with diameter (MN). When (F1) goes until the (C) circonference then, the figure define a pure Circle construction that is defined as follow:
A circle is generated by a isoscele triangle (F1PE), the summit (P) of which is a fixed point while the side (EP) is a constant length.

- règlement de construction fully (Switzerland)

- prove ellipse (Taiwan)

a) - From any given fixed point F1, draw any segment EF1
b) - Draw TP, a median of EF1
c) - Join E to F2 that intersect TP at point (P) as one of the ellipse to be formed.

Note that point (P) is the construction of the center of a circle internally tangent to (C) and to this latter internal point F1.

It is directly proved from this spatial structure of isoscele triangle that the total length from (P) to (F1) and (F2) is equal to its diameter (MN). Both are equal to the circle (C) radius as a constant length during this transformation.

Explicitly tell,
EF2 = radiusC = Constant
EP = PF1; as isoscele triangle sides
PF1+PF2 = EP+PF2 = EF2 = Constant

The altutude TP of the tiangle isoscele (F1PE) are tangent to the ellipse formed. Many others of the ellipse properties are deduced from this basic spatial structure. For example, the ellipse center is defined by the line joining the middle of two sides of the isoscele triangle intersecting the diameter MN. On this figure is shown it as line (TO) where (O) is the ellipse center.

The main principle of this transformation is that the Circle can divided itself from one central center, into two separated ones. It is the case seen for an alive cell multiplication.
When this doubling of circle center happens in such manner that the isoscele triangle is exterior to the circle (C) then, the figure transformed is a hyperbola when point (F1) is a point and a parabole when point (F1) is a line.

The 3D figure for solid surfaces, are obtained when we considered e.g. the axis (y) as an axis of symmetry.


This above five basic forms allow construction of complex composition in space. Brcause the circle is source of forms..

- "sqaureroot" + oval + inside + a + circle (, Colombus, USA)

Right! Here following is an enigma to resolved for:
The two focus center of an ellipse is not two independent indistinct things that have nothing to do each other. They have oriented meaning. The one is the Origin the other is the Birth focus. It is why an egg is born from a circle center of a hen. That is the solution of a true spatial oval egg in 2D or 3D forms!
This not a joke.

Reciprocal problems from ellipse, hyperbola and parabola

Now from any given parameters, ellipse, hyperbola and parabola, how can be found its initial generating parameters?

It is given above how from initial parameters ellipses, hyperbolas and parabolas are generated. But, in practise we meet directly any of these forms. Therefore, how can we determine their particular parameters? These are the necessary reciprocal prolems in space.

Reciprocal from conics are ignored problems in Mathematics.

The usual mathematical Geometric manners of finding tricks to get solution is no more valid. This problem need a capacity of deductive thinking needed as in Dakhiometry where all solutions are found.
So I propose to mathematicians to find solution for this reciprocal of how to find for:

a) - From any given ellipse
b) - From any given hyperbole
c) - From any given parabole

For example, from a given square surface, defined as points of ellipse or of hyperbola or of parabola, how can we determine their different parameters such that all of them constitute the fullness of this given square surface? It can be extended for a 3D volume.

The current science of the Universal Gravitation laws has nothing to do as Physics laws. It is quite an impotent fiction of man.

With deductive reasons as is for the Dakhiometry method, you will find through these fundamental problems, the true universal laws of Matter Condensation from where anything in the universe is constructed!

These are consequences of the basic absolute matter space knowledge.

- 3 + lois + universelles + du + mouvement (Lycée Jacques-Coeur, Bourges, Académie Orléans-Toursn France)

Vous pouvez la dire, sans être assombri par un doute.
Par exemple la formation d'une ellipse traduit pleinement, le phénomène du mouvement de gravitation, non pas celle de Newton qui n'est réellement que fiction, mais décrivant l'énergie d'un objet éloigné de son point de repos. Par exemple la Terre par rapport à son point de repos près du Soleil ou la Lune au point de repos près de la Terre ou un objet à la surface de la Terre, tombant sur le sol,... vers le centre terrien.

Remark about celestial mechanics according to difference of method
It seems that there is no difference between the Kepler's ellipse and the present Dakhiometry's one. Because an ellipse is an ellipse.
However, the difference is a fundamental capacity of deductive science relative to empirical one denoted as science of observation.
a) - Empirical method is to search from observations a likely and plausible forms in phenomena from there a formalism of mathematical model can be constructed for describing them.
b) - While in deductive mode for successive reasons it goes first to define the basic logic of the universe Facts. These latter when they are justly and steady defined, are used as root reasons for deduction of their consequences.
It is for example the case of the ellipse generation shown above where from a complete Matter Space definition, a rational science can define the reality of a space structure from there a phenomenon can't but be defined as such. Here observations and experimentations are only simple verifications as belonging to this defined structure.
This latter is what is known as the science goes from general view to reveal the particular. It is the contrary of the usual science empirical method that tempts from consequences to state a law.

Un joyau, une merveille de la structure de l'espace

- joining of ellipse form with rectangle (Bangladesh)

You are right to underline such construction. It is the case when we do the squaring an ellipse.

Je profite pour signaler que cette construction de l'ellipse indiqué sur la figure ci-dessus, est une lumière fantastique sur le commencement de l'univers et le commencement de la vie.
Evidemment, enfoncé comme vous êtes tous par la vieille Mathématique, croyant tout savoir parce que vous avez une panoplie de fonctions analytiques de conique, le tout renforcé par les calculs d'ordinateur puissants pour faire conquête de l'espace. Ecrasés encore plus par la croyance à vos hautes civilisations high-Tech et vous grosses têtes de Physiciens et Mathématiciens, vous n'avez cependant nullement la capacité de la pensée déductive et aucune connaissance de l'espace. Comment pouvez vous voir dans la construction que je propose pour l'ellipse, une quelconque richesse de vue sur les lois universelles que cette structure présente comme portail de la connaissance rationnelle.
Vous n'y verrez que des trucs et astuces pour en conserver quelques recettes et en faire une conquête des Mathématiques. Ce serait une injure à la raison et une malhonêteté intellectuelle que de vouloir soumettre la Dakhiométrie au carcan de la science empirique des Maths.

Je vous signale donc à tout hasard,
Que la construction de l'ellipse qui vous est exposée ici, est une vue du joyau aux mille éclats, à l'ampleur de la connaissance de l'espace.
En ce portail, les outres bien pleines ne passent pas. Vous pouvez y aligner tous vos savants possibles, les uns après les autres. Nul n'est capable d'y entrer, depuis des millénaires.

Il est temps que je mets les points sur les "i".

Voici quelques commentaires sur cette structure de l'espace Mère du Monde. Ce n'est pas ici, de la rhétorique, du barratin idéologique, du lyrisme de celui qui se pâme dans ses croyance. Ce n'est que de pures raisons, encore faut-il que chacun sait-il ce que pourrait être la raison. Et il est grave d'y voir que c'est une théorie ou un dogme de Croyance farfelue comme toute autre. Ce que je dis ici, se démontre rationnellemnt par la déduction de raison, comme tout ce qui est démontrée en Dakhiométrie selon la Connaissance de l'espace matière universel.

1) - Chacun croit que c'est évident mais, cette structure peut décrire rationnellement et précisément la formation des astres.
2) - L'ellipse n'a pas deux foyers interchangeables que l'on ne sait que faire de l'un ou de l'autre. L'ellipse a deux centres dont l'un est l'Origine et l'autre la Naissance. Les deux a des fonctions complémentaires de Création ou de Construction des lois de la matière.
3) - Cette structure de l'espace exprime la structure des lois mêmes de l'univers, dans ses manifestations de construction.
a) - Elle éclaire le mécanisme du développement complexe du vivant comme multiplication en cellules. Une étude plus complète peut y révéler l'histoire de la formation de la matière atomique.
b) - Aussi incoyable que cela paraît aux esprits de robot, cette configuration de l'espace, exprime clairement que l'ŒUF et la POULE est Un.

Ces remarques vous semblent de la fiction. Mais vous pouvez être sûr qu'aucune imagination fantaisiste que l'on prête jusqu'à maintenant sur les extraterrestres, n'arrive à la cheville de telles réalités rationnelles.

Ne vous leurez pas.
Vous ne connaîtriez jamais de telles vérités. Sachez que j'ai 70 ans sur cette Terre, parmis des "scientifiques" soildement institutionnalisés. Depuis tout ce temps, ces cerveaux-gris perdent le temps précieux à ne voir en moi que comme "plus con que lui, tu meurs". Dicton: Quand on marche la tête en bas, on ne peut savoir ce qu'est le monde à l'envers. C'est un fait et non quelques humeurs d'insatisfait de profane. Ceci vous montre que l'esprit des humains civilisés stagne au fin fond de leurs Labyrinthes Enfernals.
C'est sûr. L'homme a perdu sa seule chance UNIQUE d'être humain.

Loi du Comptage de la Dakhiomètrie

- la + somme + des + angles + d'un + triangle + est + égale + a + 180° + est-elle + absolue? (Algeria)

C'est très fondamentalle comme interrogation.
Voici un énoncé de Fait:
Toutes les Directions de l'espace sont ABSOLUES.

La raison est dérivée du Principe de Succession:
Toute quantité succédante ou précédente d'une autre quantité est une quantité définie c'est-à-dire absolue.
Ainsi, la matière de l'univers est discrète. Elle est donc absolue puisque étant finie, la matière est toujours succédante et précédante d'une autre quantité. Ceci ne s'applique pas à l'idéologie de l'Infini car, l'infini n'est pas une quantité.
Particulièrement, le point d'un cercle est toujours succédant et précédant d'un autre point. Aussi, tout angle d'un cercle est une quantité absolue. Le triangle n'est que trois points d'un cercle avec ses angles et rien d'autre.

En déduction
Si l'homme sait compter, ce n'est pas parce qu'il y a des Nombres comme modèle de l'univers. Il sait compter parce que la matière est Quantité selon le Principe de Succession. Si la matière est accessible par la quanrité, nous en déduisons que l'Espace matière est aussi Quantité, selon la quantité de succession de localisations. Il y a donc quantité de matière dans la quantité de localisation. Couramment, on le désigne par Masse en un Centre dans l'espace. C'est pourquoi,
Etant quantité, l'espace est ABSOLU.
Ce qui implique que le Mouvement est Absolu

Seul l'ignorance de la physique de l'espace, engendre l'idée de la Relativité du mouvement.

- evolution + fundamental + laws + of + nature (Spain)

Logic of dicrete matter and space as Potential Energy imply that Motion is necessarily ABSOLUTE. It is why the Dybamic definition of motion with a Force is inconsistent because a Force law is a Relativity expression according to that an acceleration is always a relativity concept. Relativity means that motion can be measured only as motion-in-background-of-motion. Relativity is generated from ignorance of space reality where this latter is a contradictory concept of Infinity in Nothingness. Nothingness is nothingness particularly it has no dimension as for Mathematics, infinity is a dimension.

Preuves expérimantales du Mouvement Absolu

A vous chacun qui est encore libre d'esprit

Je me rends compte que si je dis que le Mouvement est Absolu, vous êtes baba mais aussi, lorsque vous y retrouvez la raison, vous êtes aussi baba de constater que les théories des Savants Scientifiques et Philosophiques, sur la Relativité sont autant ignare sur le Mouvement. La Flèche de Zénon est une preuve de l'incompréhension épaisse du Mouvement Absolu. Le Mouvement qui étaient leur tracas le long des sciècles de temps perdu et gaspillé pour la construction de la vie.

Voici des exemples concrets et incontestables sur le Mouvement Absolu.

Ce qui est absolu est saisissable.
Ainsi, chacun peut prendre tout objet dans sa main. Il peut le saisir, simplement parce que l'objet dans l'univers est ABSOLU. La raison d'où découle sa propriété de l'absolu vient du Principe d'Unicité dans l'univers Discret. Seul le Discret est muni de la propriété d'être saisissable par l'esprit de conscience et par les sens de chacun.

Appliquons ces propriétés au mouvement.
Qui a déjà vu du mouvement sans objet? A moins de cauchemar, personne ne peut voir, mesurer, comprendre, un mouvement comme un objet en Soi.
Ce qui signifie que le mouvement est un phénomène de la matière objet. Il en est ainsi, de la lumière qui n'est que les manifestations de la matière en particulier.
Comme tout objet est une matière absolue, il en vient directement que son mouvement est nécessairement absolu.

Preuves expérimentales
a) - Il n'y a pas de Mouvement sans la présence d'objet matériel. On ne peut jamais prétendre attraper un Mouvement. Attraper signifie aussi Mesurer.
b) - Etant une propriété de l'objet, le mouvement est absolu. Ce qui signifie que l'on peut attrapper et mesurer le mouvement, en absolu. Il suffit d'attrapper l'objet en question!

Jusqu'à ces lignes, vous êtes encore baba sur l'absolu du mouvement. Mais, avec l'esprit moins formatté par les Savants des Institutions Scientifiques, vous vous rendiez compte peut-être que, EFFECTIVEMENT, on attrappe toujours le mouvement, dans la vie de tous les jours!
1) - Quand vous portez un litre d'essence dans un bidon,
n'est-ce pas là le bidon, un moyen pour vous d'attrapper le mouvement?
2) - Quand vous coincez l'eau dans une vallée, derrière la prison des barrages hydrolyques,
n'est-ce pas là, le moyen d'attrapper le Mouvement?
3) - Quand vous vous donnez un mal fou de produire et conserver des atomes de matière avec lesquelles, vous en tirez de l'énergie nucléaire,
n'est-ce pas là, le moyen d'attrapper le Mouvement, même rebelle?
4) - Quand l'on reçoit une baffe sur la figure,
n'est-ce pas là, une occasion de ne pas vouloir attrapper le Mouvement?
5) - Quand un athlète apprend à courir vite,
N'est pas là par le moyen de son corps, pour qu'il crée Son Mouvement Absolu, rien qu'à lui, perdant ou gagnant?
6) - Quand, sur le sol on trébuche et tombe et que l'on grimace de douleur,
n'est-ce pas là, le souhait de ne pas attrapper le Mouvement?
7) - Si vous ne pouviez pas résister aux cyclones,
n'est-ce pas là que le Mouvement n'est pas Relatif? Parce qu'avec cette relativité, on peut tuer les mouvements du cyclone, comme deux trains roulant de concert à la même vitesse, peuvent annuler leurs mouvements relatifs.
8) - Pourquoi, les bateaux ne peuvent jamais être en totale sécurité sur la mer agitée?
N'est-ce pas là, pour la même raison, que le bateau reçoit le Mouvement Absolu de la mer et ne peut pas y échapper par quelle méthode de mouvement relativiste.
9) - Quand on a rien de toutes les avantages précédentes,
N'est-ce pas là, l'absence de Mouvement, la Non-Exisrence, la complétude de la Mort?
Ajoutez [M.(vinconnue)2] dans la formule Relativiste d'Einstein,
E = [M.(vinconnue)2] + M.c2
Vous aurez incontestablement, la Mort dans l'Ignorance.

Voilà pour vous tous qui a encore quelque lumière de raison en soi-même, ce que veut dire concrètement: LE MOUVEMENT ABSOLU.

En conclusion:
Relisez ce texte en toute modestie.
Faites ce qui vous plaira, mais n'imitez pas par dévotion, l'Ignorance des vieilles Sciences de la Croyance de l'homme, qui ne sont capables que de fabriquer des moyens de Destructions de l'homme et de la Terre.

Du Principe d'Unicité des lois de la matière, l'univers est ABSOLU en toutes ses manifestations.

- mécanique rationnelle

Notez la différence immense, entre la Relativité et L'Absolu de l'espace.

- what + caused + motion + in + the + universe (, USA)

Actually. This a pertinent issue. "What is generating motion" mation is the basic more enlightening question while "what describe a motion" is only a practical one. This latter is the case of defining Force while the first is a fundamental Physics question.

- step + by + step + tp + construct + a + perpendicular + bisector + of + a + segment (USA)

- Euclid's second theorem practice (, USA)

- Einstein + la + matière + est + une + organisation (France)

On a fait un livre sur les proverbes d'Einstein comme cette expression en est une.
N'y voit-on pas que c'est une expression de langue de bois?
Une expression qui ne dit ni oui ni non. Ce n'est donc pas une pensée scientifique. Surtout que la matuère de sa Relativité, est un véritable bordel dans l'univers où Temps et Espace se tordent et se crêpent les cheveux à qui mieux mieux. Comment ose-t-on rappeler que la matière est organisation ans un monde où l'on doit douter de ses formes? Un monde de relativité où une Vitesse Constante (c), est toujours constante, même relativement à tout autre vitesse!
Dire que l'on m'apprenait qu'il suffit d'une seule contradiction pour affirmer que l'on est dans le Faux!

Un mot sur les Coniqueries

Il n'y a pas d'intention de ma part de sentiment de mépris pour qui que ce soit. De toute manière, mépriser l'Ignorance n'est pas mépriser l'homme. J'utilise des expressions de langage seulement pour tenter de secouer les uns et les autres de la léthargie qui fige le monde.

Maintenant que j'ai parlé des philosopheries de l'homme sur l'Absolu et le Relatif, on peut peut-être songer à la philosophie consistant en l'intérêt pour ce qui fait que l'homme vit.
L'appréhension du monde autour de soi selon la Relativité n'est pas récente comme inventé par un génie de science moderne. La Relativité est un défaut d'ignorance qui s'accroche à l'homme depuis des millénaires pour en faire un croyant béton. Quel est ce défaut d'ignorance qui transparaît en l'homme comme celui portant des lunettes Relativiste? C'est l'ignorance de l'universel du monde, la vérité, l'absolu du monde, en bref ignorer que le monde est un Principe d'unicité, malgré le génie humain d'inventer le mot Uni-vers. L'univers vient de l'intuition que l'homme a de l'Unicité. Le Soi, la Vérité, l'univers sont entre autes, les présences de la permanence et l'immuable du Un qui est l'Ubiquité de l'Unicité. Ce dernier n'est que l'élément ultime de logique du monde particulièrement, l'élément du Penser humain. Sa présence est si partout à la fois que l'homme ne le voit pas.
Or l'homme est un malin, intelligent astucieux, le roi du "système D". (D) comme Démerdeur, Débrouillard.
Alors, l'homme n'est pas une bête pensante. Il est effectivement une bête, mais une "bête qui Sait tout". Il sait donc la monde par son système (D) de la Relativité. Rassurez-vous, l'homme qui voyage à la vitesse de la lumière et qui rajeunit, n'est rien par rapport à la nature Relativiste de l'Ignorance de l'homme.
L'homme Relativiste ignore par:
- Le Témoignage
- L'Association
- Par Trucs, Astuces et Recettes.

Vous allez dire "mais il ignore donc tout"? Il faut une sacrée claivoyance pour faire cette remarque. Car celui qui SAIT TOUT, est celui qui ne sait vraiment rien.

Cette mise en scène d'introduction, me permet de vous faire entrer dans le monde de la CONIQUERIE. Je vous précise que Coniquerie n'a pas pour éthymologie CON et Conneries.
Il s'agit ici de vous montrer ce qu'est le procédé de témoignage conférée par la pleine croyance inculquant le tic chez l'homme de voir tout en Relativité.
La Coniquerie est la fameuse vision des mathématiciens de voir des formes curieuses, grâce aux Témoignages ou aux Observations et par associations de quoi, on a fait une science de Coniquerie.
Par débrouillardise l'homme finit par s'appercevoir et remarquer un jour, que son chapeau est un Cône comme l'entonnoir de sa cuisine ou de sa boîte à pharmacie. À force de l'admirer nuit et jour, ils finissent par y distinguer les formes que l'ombre peut créer sur ce cône. Débrouillard et Démerdeur, mais laborieux, il finit par énoncer des lois de ces formes qu'ils dénomment comme des Coniques en mémoire de la forme de cône de son chapeau. Vous savez qu'il y a qui en fait une sculpture sur son tombeau...
En conséquence, je viens de vous introduire dans la fameuse science des Coniqueries constituant les mille manière d'un cône de recevoir la lumière. Même si ces coniqueries permet aux génies de parler de leur mécanique céleste, ce n'est rien d'autre qu'une science des formalismes de formes Témoignées par un Cône.

Certain d'entre-vous auriaient la réaction en protestant que :
"Critiquer, critiquer, c'est bien. Mais, que sait-on d'autre?"

Alors, si la Relativité est Fausse comme étant la créature de l'Ignorance, il existerait donc le Juste ou le Vrai ou le Réel de ces phénomènes de formes.
En effet, le Réel est l'Absolu du monde et de tout ce qui est dans ce monde. Par exemple si l'on est convaincu qu'il y a le Soi, même sans jamais savoir ce qu'est le Soi, c'est que le Soi veut dire l'Absolu d'une certaine Réalité.
Alors, je vais vous faire ici, la danse de l'Absolu dans ces phénomènes classés sous le chapeau de côniquerie.

a) - L'espace matière est absolu, sans quoi il n'y a pas d'univers de ces astres dans le ciel. L'espace est absolu tel que les chose peuvent y être, sans quoi, personne ne peut savoir s'il y a le Nord, le Sud, l'Est et l'Ouest ni non plus qu'elle-est, son ici-et-maintenant.
b) - Or si l'espace absolu est tel qu'il est pour chacun et pour tous à la fois, il y a néanmoins des personnes qui ne reste pas en place. Chacun voit le monde dans ses Mouvements. Tout se déplace aussi.
c) - Comment peut-on décrire l'espace qui Est et l'espace qui se déplace en mouvement? Si l'on prend les obejts qui bougent comme témoin de mouvement, on se soumet nécessairement à la relativité des uns aux autres. Or si l'on ne pense au Mouvement, que seulement comme un rapport des uns aux autres, c'est que l'on IGNORE que l'espace est absolu et qu'il faut le décrire autrement que par le FIGÉ! Par exemple comme Newton et tous les Savants scientifiques, sans exception, qui n'ont que des notions relatives.
d) - Un effort pour accéder à l'idée que l'espace est fixe dans l'absolu, mais que l'espace est aussi à la fois le Contenant et le Contenu. Ce qui veut dire que le Mouvement est contenu par l'espace ou que l'espace est Mouvement. L'espace matière est donc à la fois le Lieu et à la fois le Déplacement du Mouvement
e) - La loi de l'espace univers où tout se construit sans cesse où il n'y a de Permanence que le Changement, se lit, pour ceux qui le peuvent. La loi de l'espace univers se lit directement dans l'espace, par le langage de l'espace.

Faisons cette lecture qui doit indiquer nécessairement et le Lieu et les localisations de Mouvement

1) - Déplacement en cercle
a) Le lieu se réfère à 1 point fixe F1 et un point d'un cercle de centre F2.
b) Les localisations dans l'univers de ce déplacement, est indiqué par le sommet d'un triangle isocèle intérieur au cercle F2, dont (F1F2) est la base.
2) - Déplacement en un autre type de courbe (ellipse)
a) Le lieu se réfère à 1 point fixe F1 et un cercle de centre F2.
b) Les points de localisation du mouvement sont indiqués par le sommet d'un triangle isocèle intérieur au cercle (F2) dont un sommet de la base se trouve sur le point F1 et le côté de l'autre passe par le centre F2 du cercle.
3) - Déplacement en ligne droite
a) Le lieu se réfère à 2 points fixes F1 et F2. F1 et F2 peuvent être deux cercles égaux.
b) Les localisations dans l'univers de ce déplacement, est indiqué par le sommet d'un triangle isocèle dont (F1F2) est la base.
4) - Déplacement en courbe (hyperbole)
a) Le lieu se réfère à 1 point fixe F1 et un cercle de centre F2.
b) Les points de localisation du mouvement sont indiqués par le sommet d'un triangle isocèle dont un sommet de la base se trouve sur le point F1 et le côté de l'autre passe par le centre F2 du cercle.
5) - Déplacement en un autre type de courbe (parabole)
a) Le lieu se réfère à 1 point fixe F1 et une droite D.
b) Les points de localisation du mouvement sont indiqués par le sommet d'un triangle isocèle dont les côtés sont pour l'un perpendiculaire à (D) et l'autre passe par le centre F2 du cercle. Ici, le cercle F2 peut être de rayon nul.

- the general meaning of space (, Greece)

- Aristotle + on + falling + objects + animation.gif (, Philippines)

When he tell that any object goes toward its rest point, he didn't know that he had an absolute space concept. However he was right.

- laws + of + motion + animation.gif (, Philippines)

- comment + faire + la + transformation + geometric + rotation + avec + un + compas (Canada)

Ce qui permet de définir ce qu'est un compas.
Un compas est un triangle isocèle. Il est un segment de droite (la base du triangle) ou les 2 côtés du triangle isocèle. Un compas n'est pas un cercle. Il ne peut créer un cercle. Mais le compas ne fait que reproduire un cercle. Lequel? il reproduit le cercle que fait la main du dessinateur, tenant le sommet du triangle.
Il n'y a aucun instrument réalisable qui puisse créer un cercle parce que le cercle est une forme virtuelle, dans le sens d'innaccessible. Elle est permanente et immuable en toute chose. Mais elle est particulièrement dans la main et du pensée de l'homme qui le trace. C'est pourquoi, construire une forme avec "le Compas et la Règle", ne veut dire réellement qu'une tautologie comme "construire avec le Segment et la Règle".
Le cercle est une forme transcendentale. Elle est la Forme Mère de tout autre forme. Appliquer cet énoncé à la lettre est le seul cas qui veut dire: ne pas être un perroquet mais plutôt être en conformité à la loi universelle. Appliquez le comme concept en arrière fond, en soutien de tout problème et vous verrez que des chemins s'ouvent, qui conduiraient souvent aux trésors.

Les schémas ci-dessous, permettent de construire des instruments macaniques de traçages de formes ou de courbes paramétrées. Ce que les fonctions analytiques n'en disent pas grand chose.

- fundamental symmetry principles (, Illinois Mathematics and Science Accademy, Aurora, USA)

- fundamental symmetry of the universe (United Arab Emirates)

Basic property of matter is the symmetry. The cercle central symmetry is the ultimate rest state of matter. That is to tell that at this ultimate state, there is ONLY the central symmetry logic as the unique universe knowledge, and nothing else. Therefore, the symmetry is inherent to space structure. This the permanent basic of any universal law and of human deduction process of fertile thinking.

- machanical advantage (surewest, USA)

- parabolic transformation formulas to create art (, Canada)

The following spatial formulas can be easily done in practice of Arts. For architectural drawing it can be realized with mechanic systems. There are not only compass and rules for many practical uses.
Also, algorithms for computer can produce these different line forms, in absolute situation without axis referent bothers of analytical geometry calculations. This concerns 2D and 3D mode.

- what + is + a + defintion + of + a + straight-segment + on + a + graph (, Tennessee, USA)

a) - A linear successive locations.
b) - A movement of material point according to its equidistance from two different refering points.

- A + Closed-Form + Solution + to + the + Problem + of + Optimal + Tool-Path + Generation + for + Sculptured + Surface + Machining + on + Multi-Axis+NC + Machine (, Iraly)

It may concern also robot movements where too much freedom axis cannot be easily resolved by complicated analytical linear calculations.

- Parabola math how to do it (, USA)

Here is a Dakhiometry new space consept that, may be, is yet difficult to conceive for mathematicians and physicians:
What we see as Movement in space is only simple forms and complex form structures of a material system. This is the space property consequence where form is potential energy. Therefore we should see heavenly bodies systems as fixe forms and not as random movements according to some virtual Universal Gravity. This form can be transformed under any interaction. Hyperbola and parabola are also fixe forms that don't go to "infinity". They are limited by the system energy.

- ilustration + of + motion + and + curvilines (USA)

Actually, here is how to construct real continous curvilinear lines.

- algebra hyperbola (, USA)

Algebaic calculation and all the analytical formula are necessarily dicontinous values of pararbola curve.

- The Key to Universal Movement (, Clermont-Ferrand, France)

Even these descriptions of movements are defined by space structures, its is however the basic of movement realities because placements of any object is directly defined by the ansolute space structure. Changes of object trajectories are only due to mutual interactions between them. More generally and precisely tell, changes of trajectory are interaction positioning in spatial structre for any system.
There is no uniform straight line motion according to the space Potential where movement are necessarily change of position the phenomenon of which depends to the space location energy.

- Uniqueness + vs. + universal + characteristics + fundamental (Massachusetts, USA)

- Coriolis force demonstration (, Hewlett-Packerd, USA)

The Coriolis force is born from pure imaginary.
It is false because of contradiction to mechanical basic principle that is stated as follows:
Segregation necessary happens between two simple material systems with different energies
This comes from the basic principle of matter Uniqueness where energy can define them distintively. Examples:

a) - A meteorite can never hit the Earth if these two systems is not different in energies.
b) - It is difficult to jump in or out of a running train if this latter is displacing rapidly. The energy difference is too high.
c) - Why a rider falls as soon as the horse is suddenly stopping? Because the movement energy of the rider is more greater than the horse one.
d) - Why a bullet can be launched from a catapult? Because the catapult beam is suddenly a zero energy while the bullet is moving.
e) - Why an information bit on a computer Hard Disk remains always at the same location on this disk? It is because this information bit fixly defined on the whole hard Disk structure. More generaly tell, the hard Disk information is internal to the whole material disk sytem.

The Coriolis force is supposed that the Earth is action on any object on its surface. This means that any object on the Earth surface is distinctively an independent one. Consequently, the atmosphere and the oceans are continually under strain and pressure due to the Earth rotation. Under such condition of gaing energy from the Earth as it is rotating during all the time toward East then, the atmosphere and the ocean water should necessary rotating towards the West. This whole oposite motions will necessary end a futur day since some billions of the Earth existence. May this equilbrium happens or not?
1) - If The equilibrium is not a dead end of these Earth movement then, it means that the Earth is a continual energy source. Being a perpetual energy source then there is a contradiction to the Energy Conservation prinicple. Therefore, the Coriolos Force is a false theory that ignore any basic mechanical principle.
2) - If there is the equillibrium of the two opposite motions on the Earth, then, there is no more any Coriolis-Force on Earth. Therefore, the Coriolis Force is also a false theory that states possibility of mechanical law disappearance in the Nothingness.
The Coriolis Force is only a mirage due to impossibility of the Dynamics to define movement phenomenon.

Now there is an another explaination from the Dakhiometry that classes the Coriolis Force in mirage type.
We have above an example of a computer hard Disk seen as an absolute permanent space structure where any information bit can be placed practcally as immutable structure.
Now, in Dakhiometry it can be precisely defined the matter condensation process to form any heavenly body. There is no Newton's Universal Masses Gravitation. But the matter condensation process is done according to placement of elemental matter according to ther potential energy. The potential energy characterized the absolute space location around a rest point.
It can be compared to an information bit thare can be placed in a Hard Disk. We know that a Hard Disk is logically placement of memory. It is the case for elemental matter that are progressively placed around a rest point. From the Zero Potential of a Rest point, it can be placed discrete matter successively as function of each energy.
For example, it is supposed that elemental energy quantities are denoted as (1, 2, 3,..., n). Then, from a cloud of matter that will be condensed towards the Rest point, it can be logically place successively only a layer of energy quantity (1), then when there is no more the quantity (1), it can be placed any quantuty (2), succesively the condensation process do a such exhaustion of all the elemental matter coming from their initial cloud. Any heavenly body are built by a such logical placement of potential energy. From such meticulous process any heavenly body can appear as a nice spherical sphere.
In such universal mechanical law any heavenly body is ONE UNIQUE WHOLE SYSTEM. As a Hard Disk, where no information bit can be mechanical read without loosing any memory information, any object in the Earth belong to internal system. And in rotation as any information bit on Hard Disk can not be displaced, it is the same for the Earth system where the Earth rotation cannot affect energy of any internal object on its surface. The Coriolis force is therefore only the imperfect Dynamic theory producing mirages.
Note that if between two objects on the Earth can experience mutual interaction, it is however impossible for any whole system to produce a change in his internal energy. This is only the consequences of the Energy and the Momentum conservation principles.

The Coriolis-Force and the Foucault-Pendulum are contradictories to these basic principles.

- Coriolis+force + bug + on + wheel + concentric (Michigan, USA)

The Dynamics is separated in two parts as the Kinematics and the Dynamics ones. The Kinematics is no more than the Geometry. It is a serious error when tempting to make kninematic or geometric descriptions as the Dynamics ones. Because Geometric figures can't never be described with the Dynamic Force formula. This error on foundation was done by Coriolis when he was confused in Geometry with Kinematics.

- the five basic life functions (, Honduras)

It is really such.
Because movement are phenomena of matter interactions. Universe interactions are energy exchanges not for destruction but always for construction. For exemple, from these five basic movement functions it can be deduces the oval form of an egg. The spatial construction of an ovale has nearly a structure like the yolk in a bird egg.

With the spatial language and according to the Absolute Space, orbits of heavenly body, is not observed relatively from the Earth as an ellipse form. Precisely any observation of heavenly bodies relatively from the Earth, should be as a perfect oval form. Far from the Earth this oval form can be confused approximatly with a circle. But near to the Earth as the Moon does, the orbit of this latter should appears in measurement as a pefect oval a little streched in its longest axis.

- relative motion (USA)

The one basic, the fundamental data between an observer and observed is the Distance between these two points of view. It is done when an animal is running to catch its prey. No matter what are their trajectory for each of them, it is the instanteneous true relative distance between them.
Thus, between two heavenly bodies that are in motions, the first data of measurement is concerned by the distance length between these two bodies. What are their true orbits are ignored at first by the observer but are only the consequence of some observation results.
It is why the first scientific job of an astronomer is to determine the real distances at any points of their different orbit motion. Thus when Kepler state that the planets observed through telescope are elliptic orbit, it was only a theorical illusion. He should at first only determined the distance-orbit between two particular planets. Then theorically concluded that they may be orbiting around the Sun according to deduction from the observed relative distance-orbit from the Earth.
Such steps of observation is the true one. There is no other possibility else than pure imaginary theorical prejudice method.
Therefore, the first scientific process is to determine heavenly bodies orbits relativeley to the Earth observer that may be shematically shown in the following figure.

- Relative motion (United Arab Emirates)

Note the difference between these figures from the empirical reltivity of observations process that furnishe until now all the science theories, e.g. the Newton Force.
The relative heavenly bodies orbits are denoted as relative but is not the mirages from relativity concept. These relative orbit are rather the absolute considerations of measurements. Because the measurements of distance between an observer and a given object are a true absolute length recording. Obviously space is both distance and direction, therefore, a distance plus a direction furnishe a trajectory description as orbit. This is necessary the real measurement condition. Because an observer from the Earth can never practically see directly Jupiter orbiting around the Sun. The Jupiter elliptic orbit is only a theorical consequence from practical observations.

- examples of absolute and relative motion (Mlaysia,

Relative motion This next figure show the relative motion that contradic the Coriolis Force.
Observation point (M) in rotation around point (O), should see a point (P1) and (P2) according to relative trajectories (T1) and (T2) as in oval forms.
a) - (P1) is independnent to the rotation sytem but is absolutly fixe.
b) - (P2) is also independnent to the rotation system, but it is mouving in a linear and uniform motion. It relative trajectory from (M) is also a nearly oval form but not as a circle or an ellipse.

Mouvement relatif Note
An artificial satellite with circular orbit around the Earth is only an absolute one. But relativeley to an observer standing on the Earth surface, the true observed orbit of this satellite is as shown in this next figure. This latter shows the relative orbit of a stallite at 1000 km altitude seen from a signal collector fixed on Earth. The reality of hevanly orbits are Absolute ones and prove that tne space is absolute. It is why the Einstein Relativities contradict the universe reality.
Relatively from a fixed point on the Earth surface, any artificial satellite should have rather an oval form!
This relative trajectory is not a virtual one calculated from an analytical algebraic function as it is done with the Coriolis force. From spatial construction the relative locations are real defined data. In such case of relativity, this shows that the Coriolis force is a bad artificial theory.
The trajectory shown here is only the basic general form. According to the velocity of any object launched from the Earth, its relative motion "discribes" the same form according to a particular homothetic one. So, until now some weird thing, particularly about gravitationnal interpretation, from observations on satellites, probes and planets trajectories come from systematic error when using the Newton's, Einstein's and the Coriolis' inconsitent and false theories.

- physics gif animation relative movement (Serbia)

- translation + and + rotation + superposition (Germany)

Yes it is exactly the case.
It concerns not the Dynamics but only by the Cinematics. It is an error that contradics the theory and complicates the formalism when Coriolis introduced there a Force. This latter states a false physic concept that between two independnent objects, there is an interaction Force. We get there the contradiction to the First Newton Law. Even if the Universal Gravitation is a curious oddly exceptional Law that has a privilege to contradic the First Newton law.
All this show that the Newton's Law are incoherent and fondamentally unvalid. It is terrifying that science of man is so blind and thus very adaptable to contradiction!

- the + observed + motion + of + an + object + not + only + depends + on + the + position + of + the + object + but + on + the + position + of + the (, Michigan, USA)

Yes the two motions should be composed in the total relative one.
Yes the two motions should be composed in the total relative one.
It is why when we mesure only the distance between the observer from the observed object while donot know the observer motion, the result will be a virtual one.
Unhappily, it is the case for all the measures done in Astronomy!

The Force that is a Relativity view point theory is true a source of illusions.

Mouvement relatifHere next is the trajectory of one point (P) seen relatively from an observer (M). The two trajectories are perfect circles. The frequency of (M) is twice the (P) one.
From (observer (M) the trajectory of (P) is no more a circle but seems to be an ellipse. However, it has not the ellipse symmetry. More, the relative (P) trajectory is not symmetric between its two half-cycle.

The next figure is the construction according to basic reasons perfectly defined and not with hazardous imaninary. Also, it is not done according to the old Analytical Geometry. It represents a same {M;P} system in two absolute circular orbit where the cycle of (M) is two time the (P) one. Their orbits are not concentric.

Mouvement relatif The relative (P) orbit observed from (M) is not a circle form while it represent the exact distance observed between this two points. It is what should be measured if an experimetal technique can perform it.
The system {M;P} may represent an equivalent of real planets for example the orbit of Mars seen measured from the Earth. These two are turning around a center near the Sun.

- Kepler Mars orbit non opposition (

- diagram of pregnant woman (Alaska Airlines/Horizon Air, Alaska, USA)

- sun orbit of Lebanon (Australia)

- Ho-Chi-Minh city wind diagram (, Vietnam)

- pregnant woman body diagram inside (, USA)

- golden communications group Ho Chi Minh game show producer (Malaysia,

Mouvement relatif

This next figure is a diagram for orbital type of Pluto around the earth. This shows that all the Solar planets have an relative orbit around the Earth not as an ellipse.

Mouvement relatifHere is the type of Sun orbit relatively to a given point on the Earth during an entire day if the Sun center is considered as fixed. In this case, the Sun orbit is exactly an oval form. During a entire year this orbit will not be a continous but a not closed form. Its curve will be as a point on a running wheel but this latter should have an oval form.
It can not be concluded that at midday the Sun is nearest than during the night because of the Sun distance. This difference is negligible because the Earth diameter is too small relative to the faraway Sun.

From this real trajectory according to the real distance between the earth from the Sun, we can note that the time of Hot-Sun is shorter than the one of cooling Night during the Earth's 24h. Then, the hot-house effect is quite invalidated. This so-called effect is more pronounced when we consider this trajectory of real distance during a whole year duration.
Consequently, on Earth it is the globe law as ring structure that furnish a perpetual energy activity. There is not the Earth hot chore of magma that is created by the Newton Gravitational law. A globe structure is only deduced from the matter condensation process that in turn, rests on the Absolute space potential/rest-point principle.

Note All these relative may seem too strange to you because until now they are not mentionned in Astronomy.
However, these orbits are the everyday truth and practised by everybody. For example any team playing ball are practising and mastering such complicate relative trajectory. So when one run after a ball, the one main thing is to look after this ball without worrying about its trajectory form. While really, the whole ball trajectory is the most complocated one. In fact the heavenly body relative trajectories are the most simple as shown above.

All these spatial constructions of relative trajectories are reversible. This is to say that if a relative trajectory is précisely measured then, the absolute initial orbit of a heavenly body around its rest-center can be deduced from there.
For example, if the relative orbit of Mars or Venus are measured then their absolute orbit around the Sun can be defined. It is the possibility for any star if their distance from the Earth can be well defined. Therefore, science can proved that the Earth is not the Universe center. Until now all the heavenly bodies orbit are defined theorically using the hupothetic Newton's Universal Gravity as foundation. It is a false method to search object location by the masses.

From this result, we can see that there are always stange behavior in the different planet orbit, if astronomists are supposing that all the planets of the Solar sytem are theoricaly a circle or nearly an ellipse. From there they use the Relativity theory to justifyed any of this strange orbital behavior.

This should be applied to any satellite around the Earth. The deformations are more pronounced if the absolute orbit of the satellite is an ellipse one. The distorsion is more imprdicable when the ratio of their rotation frequency takes any value.

This trajectory of relative motion between two points is precisely contructed according to space structure. It shows that the Coriolis Force equation is a false one.

How the Dakhiometry can define rationally a parabola

- projectile goes 16.5m at 15 degrees above the horizon how fast was it going (USA)

Any parabola trajectory parameter can be determined easily by spatial construction.
For such conditions, if friction in this trajectory is negligible and the impact point is on the horizontal plan of the launching one then, we have:

Horzontal speed = 17.6043 m/s;
Initial energy = 310.1313 J/kg
Horizontal efficient energy = 309.9117 J per 1kg
with a lost of the initial lauching energy of about 1/1000
Total trajectory time = 0.9372 s
Height of trajectory = 1.0772 m

All these values define the parabola inscribed in this two given data. Also from given initial energy and angle of trajectory it can be determined precisely and simply all the other such trajectory characteristics.

- algorithms and analytic geometry (Brazil)

These old mathematics methods are approximations of empirism human manner to get an approach to realities. The reason of this man working behavior is because he never had some knowledge on the universe matter characteristics. The Nothingness had produce ignorance of the Space Physic even though this latter is the basic concrete matter of knowledge for science. All what are denoted in Mathematics as the Conics are really a poor science sigth on the wealthy space. The Newton's laws that gives rise to the modern sciences is an example of a deep ignorance on the matter prpoerties. If man wish for going further into extra-terrestrial space he has to change all his manner to get a more rationnal approch to true Astronomy else than with the erroneous and monotonous so-called Universal Gravitation by Masses.

- a + scientific + that + do + work + "whith" + law + of + motion (, Conroe Independent School District, Texas, USA)

- diagram of the overall universal law (, USA)

- Representation of addition and subtraction movement (United Arab Emirates)

- Naruto five "mation" (, Washington dc, USA)

- types of basic motion graph (Malaysia,

- basic rigid motions of the plane (, Monmouth University, New Jersey, USA)

The following figure shows the five basic FORMS seen as movements.

5 Basic space structures for motion

Figure resumes the Five Basic space stucture for universal laws of movement.

Voilà comment, en se débarrassant de la Relativité comme une propriété de l'univers,
Il Faut décrire l'Espace de l'univers, au-delà de toute notion de figé de l'espace et de préjugé relativiste du Mouvement, car l'espace est à la fois Lieux et Mouvement. Il n'y a pas de mouvement en soi, tout comme il n'y a pas de Temps, pour courir derrière son ombre.

- geomatrical animation compass (Sri Lanka)

- line circle journeys (, UK)

- Changing + Universe + Concepts (, USA)

Do you know why it is difficult to build a steady aeroplane as an unique wing system?
It is because its straight line trajectory is not generated by two fixed independnat points as stated above in the first case of motion generation. An classical aeroplane with a long tail can realize two independent points in space. While an unique solid wing whatever its forms, is only one point. Because a solid system has only one center.

- according + to + physics + + 2 + stone + one + 5 + kg + and + other + 10 + kg + if + we + leave + these + from + hight + which + one + is + come + down + first (United Arab Emirates)

According to natural law defined in Dakhiometry, if friction is neglected,
1) - The two masses is the first down because there is no last arrived.
2) - The two masses is the last down because there is no first arrived.

In conclusion
Potential between Location in space ignore the mass quantity hierarchy.
Absolute space means that a same Potential corresponds to a defined distance and inversely, whatever is the distance direction.

One uses to tell: what a paradoxical law. Because one uses to think the conventional Force, as the mass time the acceleration of an object...

Maintenant, quoi d'autre?

Extirper les esprits des vielles croyances millénaires est un horrible boulot. Car, si l'homme a son esprit capable de penser par déduction de raison, tout ce que je dis dans mes textes, se complètent en étendus lumineux par eux-même.

Vous avez vu ici, que l'espace matière est à la fois Contenu et Contenant. Ne demandez-vous jamais pourquoi il y a la Cinématique et à son côté, la Dynamique, tous deux séparés par une dichotomie newtonnienne? Non, dans léthargie, on ronfle mais on ne se demande rien d'autre que ce qui plaît ou ne plaise pas à son nombril. Ce qui prouve que le science Mécanique est un résultat direct de l'empirisme des esprits persévérant dans sa capacité de Tâtonner. D'ailleurs, la Cinématique et la Dynamisme sont acceptées comme telles que parce qu'elle fait la brillance de Grande Science, plus grand que ça, tu meurs.
Revenons aux raisons en considérant que l'Espace est Contenant et Contenu.
a) - Le Contenant est ce que je viens de définir ci-dessus, comme structures de localisations supports ayant son immuabilité comme propriété de l'espace.
b) - Maintenant, il est nécessaire de voir quel est son Contenu. Dans mes illustrations des 5 structures d'espace pour le mouvement, il y est noté la présence générale d'un traingle se référant à deux centres de références.
Alors, Le Contenu de l'espace concerne la Matière Condensée des constructions de l'univers. La Matière Condensée est régie par les lois de Potentiel d'espace. Ce qui veut dire que la Matière Condensée est NECESSAIREMENT descriptible par les énergies. L'Energie qui est espace, s'exprime aussi par les éléments d'espace.
Alors, il y a longtemps que j'ai exposé en mes textes de ce site-ci, ce qu'est le théorème de:
La Structure Triangulaire Générale

Ce théorème que chacun de vous cite comme le théorème de Pythagore. Il n'y a pas de plus grand sacrilège de spoliation d'ignares! L'Ignorance ne pardonne pas mais aussi, elle ne se pardonne pas. Parce que vous croyez être cultivé et diplômé en Math...

celui qui permet d'entrer dans le monde de la Connaissance, en homme adulte, sevré de ses Dieux.
Ce théorème permet de voir l'espace dans son aspect Matière Condensée qui génère le phénomène MOUVEMENT.
J'ai donc explicité la généralité de la matière univers avec sa propriété double de Contenant-Contenu. La VRAIE science Dakhiométrique permet d'embrasser les phénomènes de Construction du TOUT univers.

Allez-y avec vos formules et baguette magique appelées Théorème de (Pythagore, Thalès,... Newton, Einstein,...). Avec la vue Relativiste de vos Dieux, dites moi ce que vous voyez à votre l'horizon. Je crois que le fond d'un puit, ça s'appelle une impasse!

- mécanique rationnelle

Notez la différence immense, entre la Relativité et L'Absolu de l'espace.
La mécanique rationnelle est issue d'une contradiction que l'on ignore. Elle est issue de:
a) - La Cinématique est absolue, parce que les considérations mathématiques sont toujours Absolues.
b) - La Dynamique newtonnenne est une pure Relarivité. Avec les meilleures volonté, on ne peut vraiment pas le nier. Il suffit de regarder les définitions de la Force. On le sait très bien, sans jamais oser la regarder en face. La Référence Galiléenne le montre clairement comme référence relative. La mécanique rationnelle ne peut rien faire sans ses références. Les contorsions de la Relativité d'Einstein sont les symptomes de l'apogée de ces tourments de Référence Mécaniques. L'exemple de l'impasse Relativiste est illustrée par le théorème de d'Alembert avec la force virtuelle mais surtout celui de la Loi de Mondre Action de Maupertuis, qui ne dit rien de commode et de pratique pour la mécanique rationnelle. Cette confusion est illustré par la Principe Optique de Fermat qui ne sait pas qu'il lui faut une référence absolue et non la relativité d'une vitesse.

Aussi croire que la mécanique rationnelle est non-relativiste est une ignorance que l'on ignore, parce que l'on a fait un cadre d'or pour la Cinématique, ce borgne du couple borgne-aveugle.

- decimal + system + of + measurement + whose + units + are + based + on + certain + physical + standars + and + are + "sacaled" + on + multiples + of + 10 (, Mexico)

- Draw a segment of 6.4 drawing (, Italy)

Here is how to draw any decimal length, provide that a unit length is defined.

any precise length With the usual Thales property it can be constructed any decimal length in the unit defined.

Then, any given decimal length can be constructed. Scale problem is resolved according to homothetic construction.

Note that not only decimal is concerned. There is general method of construction. Any length can be obtained as part of an unit length. It can be defined rationnaly et precisely by construction. There is no "hole" of constructions in the succession of a length. It is to state that there is no irrational quantity.

Note that the inverse
(2/1.36...) = 1.47
should be done according to this process on figure and not as what was done by Euclide using Number names.
Here also, the Dakhiometry has a general precise but simple method to do divisions of length quantities.

- logic + division + axiom (The University of Utah, USA)

Actually. It is the idea of how was stated the Euclide's Division Algorithm. We can see that this is mostly a congruent problem and there are few rational solutions.

- Destiny + "Cululate" (


- the + sum + of + three + times + a + number + and + 7 + more + than + the + numver + is + the + same + as + the + difference + between + -11 + and + twice + the + number + what + is + the + number (, Florida, USA)

A strange concept on FORM

- prove + a + circle + fits + in + any + triangle (Champion Technologies, Chimical Company, West Texas, USA)

It is a basic intersting problem. However, one should pose this problem in it inverse manner. That is to ask why a any triangle fits in a circle.
Because there is no independent form denoted as Triangles. Really there are only three basic forms. They are: Circle, Square and Polygone.
1) - A triangle is only a circle because 3 points always belong to a circle. As one tells it, a triangle is a Three Angles. Angles are property of circle Directions. What we know as properties in a triangle are the ones of the circle.
Note that if one knows that a triangle is in fact a circle then, it is very easy to resolve spatially the Morley's theorem.
2) - What polygon is inscribed in a circle? It does if all each set of 3 vertices are inscribed in a same circle.
We can see now that really there are only TWO BASIC forms: the circle and the square!
3) - But we can do more:
There is only ONE UNIQUE Basic Form: the Circle. It is because a square is no more then two rectangular triangles!

A circle is not really a form because it is only the remanence or the persistence of vision or the memory of the matter space before the beginning of the universe construction. A cirlce is only a BASIC LOGIC of space!

What is unusual but wealthy view point on space structure or space as Potential Energy.

Hereafter are texts on the Dakhiometry,
a rational method for determining properties of the dakhi, the Breath of the universe ...

The dakhiometry, text DK001EN   (sep 2001) The Simultaneity and the Conservation are notions of the Permanence of the universe.
The dakhiometry, text DK002EN   (oct 2001) The memory-universe built in respect of rigorous conditions, but with simplicity.
The fundamental concepts in the Dakhiometry  (nov 2001) In dakhiometry, universal laws and phenomena show surprising wealthy relationships. The future physical Laws are not yet established in the universe of nowadays.
The Accuracy, the Certainty and the Doubt  (nov 2001) Mathematical accuracy is a mechanical process while Certainty and Doubt are the engine of the evolving Self. Some analysis of the Non Euclidean contradictions.

Proof of the Fermet's theorem  (mars 2002) Equation xn+yn=zn, has no solution....

Cyclone formations  (mai 2002) Cyclones are phenomena attached to the band structure of the atmosphere winds....

The First action of the beginning of the universe  (sept 2002) How to square a circle. This surface transformation is the first natural operation at the beginning of the universe....

The Proof of the universe Evolution Process  (oct, 2002) The beginning of the universe construction used the squaring a circle to allows the central symmetry to establish the left-right symmetry for the alive.

The Proof of the squaring a circle  (oct, 2002) Proof of the surface equality after the squaring a circle.

The basics of Matter. The proof of Thales' theorem. The proof of the Pythagoras' theorem.   (oct, 2002) Properties of Matter allows to state some foundations on the knowledge. From these bases, simple proof can be done one the Thales' and the Pythagoras' theorems.

The Archimedes' Property  (jan, 2003) The Archimedes' property was used by the resolution of the circle perimeter that was attributed to Archimedes. Analysis are done on this resolution. This axiom is very used in modern mathematics and some confusion are commented.

New Proof of Light Refraction and Reflection Laws  (dec, 2004) New Proof according to the Dakhiometry method that shows that light is not a particle and a wawe that may have a trip of 13 billion of celerity distance...

New Proof of Light Refraction and Reflection Laws  (dec, 2004) New Proof according to the Dakhiometry method that shows that light is not a particle and a wawe that may have a trip of 13 billion of celerity distance...

Properties of circular structures and their consequences.  (jul, 2005) This page introduces the contents of a work that constitutes the foundation of the Dakhiometry...

Liquid Archimedes' property an the Potential as gravity.  (jul, 2005) Statement on Liquid proerties and object Potential energy as the consequences of the condensed matter process localisations...

Archimedes' gravity center volume measurement method.  (dec, 2006) Proofs of solid aeras and volumes measurements, was all unsuccessfully done and quite erroneous works...

Unbounded Energy Source Engine (In French)
"Le Moteur Source d'Energie de tous les temps"
(Aug, 2006)
An application of the liquid law new understanding to build a machine producing energy of high capacity. A reality for the near futur.

Succession allows Quantities. Basic of Counting.   (august 2007) Unity Succession Principle is the foundation of the universe Fullness. fullness is necessarry to allow Quantity. Quantity is Reality of the World existence.

More detailed analysis written in french only:
Succession and Quantity analysis.

DOUBLING A CUBE.   (2011/2012)
According to the universe principle of Matter Conservation, any construction in the universe is done by matter Transformation. The Squaring a circle, the Angle Trisection and the Doubling a Cube are the basic exemples of such space property.
Incapacity of solving such bases, man cannot claim to have a sufficient knowledge level to be abble to build a true science.

To read more aspects on this theory,
texts archived : 
Archives : free download

Correspondences :


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