Analysis of the Archimedes' Property used for the calculation of the circle perimeter

Analysis of the unfeasible of the Archimedes' axiom to resolve a problem.

Nguyên Tân Tài

Preamble

It is shown how Archimedes' resolution did not applied the axiom. The reason is that this axiom is not applicable to an unknown variable. Therefore, the Archimedes' exhaustion is an undetermined method that drives to the untrue solution.

At first it is presented the spatial property of the space according to the first postulate of the Dakhiometry on the matter. This means that anything in the universe is rational and perfectly determined according to the space property. Therefore, any unknown variable that one has to resolve must be contained in the initial data of the used algorithme. The first rule of solvating a problem is to find a solution hidden and not a solution from nothing. This rule is not so obviously respected. And in the exhaustion method of Archimedes, we will see that the unknown circle surface come from the Nothingness.

It is shown in the end of this text that the theorem on the Archimedes' property used in modern Number Theory has also an untrue proof.

The Space according to the Dakhiometry

Remind

The quantum Matter is :

1) - The Space
2) - The Recurrence of space
3) - Defined in particular objects as a number of quanta of matter.

The Recurrence of space is the matter property that allows the construction of the universe. Interactions of matter obey to laws in a universe plane. And constructions are in succession of diversified planes.

Now, the foundation of knowledge is based on the quantum consciousness. The quantum consciousness is the property of the Space to be a whole of the absolute determined locations. Thus, quantum consciousness is the property of the spatial differentiation of each location. We can say that each spatial location is a unique event in matter. And generally, we can say that each location is the reality of a Being notion.

The space is the whole universe. In quantum matter, any spatial location is separated from a next one by a quantum of length that is denoted as a minimal distance of the universe. Consequently, the whole universe is a succession of quantum distance.

At the beginning of the Evolution in the universe, a transformation of a perfect central symmetry principle into the possibility of angular forms of a square had launched the Recurrence in diversified directions and thus allows the beginning of the universe construction. Interactions of matter are phenomena between two different objects. The minimal phenomenon is thus the event of a spatial change of location.

Because that anything is a matter construction, the minimal knowledge is an event that is necessarily a quantum spatial location. With the Recurrence phenomenon, and a quantum of spatial location, the Whole universe space is considered as the natural foundation of the Induction Principle. Thus, starting to a quantum spatial location, we can make a trip in the whole universe as follows :

1) - A unit of knowledge event belong to the Space
2) - Any event is necessarily at a spatial location
3) - A next event is at least a next spatial location.
4) - Therefore, any next event in the universe happens necessarily in the Space.

As the space is absolute determined locations, any event of interaction is necessarily determined. For the whole matter, there is no Unknown event.

This is why Matter is a Principle of the universe construction that is the Permanence. Constructions are projects and resolutions of projects. This are the view points for any objects in the uniqueness. But as being the Permanence, the Matter has no problem and no solution to seek for. The Whole universe has only TO BE. Exactly, Matter is Solution. It is the basic Reason that everything tempts to learn from the nature. Practically for human, the aim of the knowledge stays in the nature. When human tempts to resolve his problems, in arts or in sciences and one says it as a "creations" or inventions, he tempts fundamentally to reveal what is yet in the nature. This is because the Matter is also a Permanent Solution.

This matter properties seams so mysterious and humann began to explain that in Believes. Now, we have only to take the consciousness that a Whole is necessarily Solution of Life, and the Permanence Principle of Matter has the consequences of unbounded solutions for uniqueness. These remarks are deductions from the Principle of Unity and fit well with the reality of everybody.

The Dakhiometry is not only for talking. The Dakhiometry is the rational knowledge of the Breath of the quantum matter. It is not built on formalisms but tempts to recall everybody to take consciousness of their natural capacity of knowledge, their large intuition of the nature, this wealthy part of themselves that are their natural complexity of construction.

For knowledge, there is a most simple model of knowledge that one can find in the natural number series. Why are there numbers ? This come from the Principle of Unity that knowledge is only possible from the discrete matter dakhi. And the discreteness allows the uniqueness of quantity that we call numbers.

Where can we find the reality of numbers ?

This reality is not in writing numeric symbols that are the complex capacity but we do not forget that they are only language inventions. The reality of numbers is found in the Spatial structure. And the Dakhiometry reveals this spatial structure situated in a whole universe plane where one can read any series of numbers. and more of unknown series that are still unknown. In this spatial structure numbers are disposed such that any calculations are straight forward. It is why the Matter is Solution is a nice and True concept. It is why human can hope that with the evolution that enlarges to the whole humann of the Earth, their knowledge of matter is such that the human uniqueness can gain a vast rational vision of the universe. With the evolved human the complexity of the life problems can be quickly resolved owing to his capacity of more large consciousness of the universe Matter.

In Conclusion, the principle of the Rational Knowledge can be said as follows :
In the universe any problem is necessarily solvable. And the method of resolution is not to reveal any unknown phenomenon from nothing but to combine relevant particular data from that a solution may appears. The physical problems are solvable only with an existent solution that is hidden at the moment amongst the data. If there is no preexistent solution, the problem is necessarily unsolvent.

Analysis of the Archimedes' resolution of the Pi value

The above introduces to the Archimedes' Pi resolution. We will see in this method that there is not possible pre defined solution. It appears that there is a real great confusion.

The Archimedes' property

- controlled + and + convergent + approximation + for + exhausting + the + circle + by + polygons (Canada, Québec, Montréal University MacGILL)

The Archimedes axiom concerns comparison of two length. It can be said as follows :

Between two given different lengths, G is the greatest and L the least :

1) - G can be shorter than L if one subtract G successively with more than the half of his current length.
2) - Inversely, L can be longer than G, if one add to L, successively more of the half of his current length.

Important comments:

Note that this axiom concerns precisely two perfectly defined lengths, the G and the L one. Manipulations and comparisons are possible if, and only if, they are done on precise defined lengths.

Fig-1
This figure shows the Archimedes' property of lengths G or L to be shifted relative to a defined reference length. The upper of the figure is to shift G to shorter than L. The lower part is how one can shift L to longer than G.

Now we try to apply this axiom to seek the perimeter Pi solution. Archimedes have used a multiplication of the polygon edges to converge it to the circular perimeter. Thus, if one apply the above Archimedes' axiom, one must use :

First - a polygon (P) inscribe in a circle (G)
Secondly - define a circle (L), that the perimeter is greater than the polygon and less than the circle (G).

Fig-1-1
Let us have a try to do the only process that Archimedes should use to seek the perimeter of a circle. The resolution is done according to the Archimedes' property and the exhaustion method. The blue polygon (P) must scan a path starting from a blue equilateral triangle polygon that should have a less perimeter than the red circle (L). Then it must be enlarged after some iterations, to be greater than the red circle. The main problem is to know how the polygon is less or greater than the circumference of the red circle. The black circle (G) is only a guide for the polygon enlargement the limit of that must be obviously greater than the red circle. On may note that even if the Archimedes' method is successful, the exhaustion can not go further than some few steps. Therefore, the accuracy of the result is not very good, provide that the comparison of the polygon with the curvature of the circle could not be enough fine.

That is one must know how to compare the circle (L) with the polygon (P) and also with the former circle (G). For circles comparisons it is easy and obvious. But how can one compare the reference circle (L) with the polygon (P) ? That is to say, one must know the solution before finding it !!!

- Archimedes pi (USA, The University of Northern Colorado)

The Archimedes' axiom above mentionned is irrelevant in two manners:
a) - One cannot converge anything toward nothing.
b) - Even if one suppose that the two polygons meet at a same perimeter, it is not proved that this perimeter correspond to the circle one.
c) - In Dakhiometry, it is really proved by spatial construction that the two polygons really meet precisely at the circle perimeter. However, this proof needs to know how and where this circle is precisley defined. That is to say, if we know how to define a circle, we don't need to search it with two polygons.
d) - In conclusion, if we know how to determined a circle this means that we necessarrily do it ONLY through the squaring a circle construction!

Fig-2
Applaying the Archimedes' axiom to find the perimeter of the circle (L). Here we try to place a circle L with the unknown perimeter between a circle (G) that circumscribed the polygon (P). This latter must be less than the unknown circle (L)...

Now as one say in mathematics, we supposed the problem resolved ! This means that we can apply the axiom to stretch the Polygon (P) until it has a greater perimeter than the unknown (L) one.

Ok? Let us go ! .....

Somebody can learns me how to have the consciousness of the a Greater or a less polygon relative to an unknown circle (L) ?

We stop here the analysis of this problem, not because of lacking methods but because no arithmetics operations and no comparison are possible with the unknown

In summary :

Rationally, it is impossible to assert that one can construct a polygon that the perimeter must be less than the one on a UNKNOWN circle and in the next, to concluded that this polygon is greater than this unknown thing. Now, what happens for a comparison, between (P) and (L) ? We must do as following :

With (P)-(L), there are 3 solutions possible : less than Zero, zero, greater than zero

With (P)/(L) there are 3 solutions possible : less than 1, equate to 1, or greater than 1

We apply this method to the perimeter problem and replace in this relationships the real nature of the (L). Then, :
(P)-(UNKNOWN) ???

(P)/(UNKNOWN) ???

Therefore, there should be no possible solution when using the Archimedes' axiom that need determined data.

Now one can try to do this problem, in using a polygon that initially is greater than the unknown circle (L).

Fig-3
Archimedes used the exhausted method to converge the polygon toward the unknown circle in the two directions as stated above. We try to do it according to the axiom but the problem is not in the method but in the manipulation of an unknown variable as in the first case at the figure2.

- Archimedes Method of Exhaustion (Guam)

- Archimedes + applied + mathematician (Spain)

- converge + toward + never + touch (UK)

- circles with polygons touching the sides (USA)

Conclusion

The Archimedes' property was stated in its form as a property of length or numbers to be extended. And this extend validated by a comparison process between two defined lengths or numbers. Therefore, this property is true as long as it can be verified by comparison of known variables.

Therefore, with an unknown variable, the comparison is impossible. This axiom is always true, according to the unbounded natural number series, we can say that stretching a length we can get at least a more greater or less length relatively to any given length.

But only this property of Greater or less than. Because the order is a quality and is not a number. To be greater or less than something, do not allows to know this thing.

Therefore, in this particular perimeter seeking, the Archimedes' axiom, can never give the knowledge of the perimeter of the circle.

How this problem was resolved by Archimedes ?

If related documents on Archimedes are exact, he do not resolve this problem according exactly to the axiom. There is something that is very confused. As shown in this next figure4, there is only the polygon (P) inscribed in the circle (G).

The necessarily unknown circle (L) must be represented but it is not used for comparison. At least, to predict the Greater or the less than. This step is foudamental. A result is retained here, stating that the polygon must be greater than the unknown circle, that is not here, and we read then that the polygon is necessarily less than the circle (G). It is said then that is a contradiction. This is false, because the polygon is always less or equate to the circle (G) and this latter have nothing to do with the unknown circle.... This is very confusing. If these documents on Archimedes are destroyed during their histories then this is the explanation. But this seems not the cause, Because the same reasonning is done in the two directions of the convergence.

Therefore, we can concluded that Archimedes had not used this so called axiom, as he had seen that this axiom was not practicable. He had then done the resolution of this problem with an empirical experience on many figures...

According to the description of the Archimedes' resolution of this problem, it appears that there is no logical reasoning. And we may suppose that the Pi value given by Archimedes was only an empirical measurements on figures. And this conclusion seem probable because this so called Archimedes' Axiom is impracticable for resolving problems. This axiom seems to ne valid as it, because it referred to DEFINED Variables. But as soon as one tries to apply it to find a solution of problems then one of his variables becomes unknown and the Archimedes' property is useless.

Fig-4
The text of the Archimedes' solution for Pi seems very confused. The perimeter of the unknown circle is not represented. Only a circle (G) used to circumscribed the polygon was used a contradiction argument, that have nothing to do with the solution. And more, this circle (G) is considered as the unknown circle, at the end, to conclude to a contradiction that the polygon should not be greater than it. This is not true because the problem is to compare (P) with an unknown circle (L) that is not there. This is completely false as we look at figure-2 and figure-3. There are necessarily two independent circles to be able doing analysis.

There is something more strange that we must say it. According to the axiom, the initial and the modern one, one must scan the polygon perimeter with {n time P1}. P1 is denoted as a part of the perimeter P of the polygon. On this figure of the so called Archimedes' resolution, there is really and increase of a part of P. But this is done with : {P1+P2+P3+...}. That is to say that these part are variable and do not obey to the axiom procedure.
However, even if one do {P1+P1+P1+...}, the polygon perimeter will be rapidly greater than the circle. This means that one can not get a polygon of more than a ten edges. Therefore, if Archimedes had found the value of Pi with more than 70 edges for the polygon, this should be done only in the convergence procedure that tempts to approach the equality of the two different figures. Archimedes had thus probably doing so, provide this axiom is unfeasible. Archimedes had probably found experimentally an estimation of the perimeter value. And this text of the so called Archimedes' resolution may be done by an another unknown author, during the next centuries.
But how is it possible that one had ignored all these big contradictions and lacuna, through the analysis of so great mathematicians generation, according that they had done this, as their basic foundation... ?
- archimedes + text + manipulation

In this text about the Archimedes resolution, the circle (G) is not the sample (L) of circle to seek the perimeter. (G) is only a guide figure to be able to multiply the edges of the polygon (P) because (G) is a limit defined for (P). And there, (P) is always less than (G). The main problem is to compare (P) with the sample circle (L) from that one can concluded that (P) is greater than (L). With no reference sample to measure, how can we make an approach for the polygon edges ? We can pose that P is probably greater than the sample (L). But where to place or what is the value of the (L) ? and the fact that any polygon perimeter is always less than the circumference of the circumscribed circle, is not a contradiction that allows to conclude the equality of (P) with ANY sample circle ! You are on the top of the Everest and thus, higher than any top of house or building. On this fact, can you say what is the precise height of any of this house ?

The dichotomy algorithm
- dichotomy ++ algorithm (Cuba)

There is a wide useful method in the informatic and computer technology. This is the dichotomy algorithm for seeking a file among a list. It consists to find rapidly a particular file in a very long list. The algorithm proceeds to determine this particular file with a method as the Archimedes' property one. Thus, it compares the place of this file with the greater or less process. And during some of these global iterations, this algorithm converges rapidly to the precise location of this particular file. The Archimedes' property is quite respected here and the method is successful.

But why can we not apply this algorithm to the Pi value seeking ? This example is the obviousness of the error for the Pi problem. You may note the main difference of application. In the algorithm of file seeking, we have a PARTICULAR File, that one have to find. One must enter first, the precise references of the file into the algorithm input. And there, the ordinal numbers of the list are also known. In brief, any variables in this practical method are precisely known. Therefore, it works well. It is not the case with the above Pi problem. Because the Pi is precisely this "particular File" to find. But there is NO PRECISE reference to define the variable Pi in the algorithm method input. Also, there is no precise ordinal numbers where to class the Pi File in a list of this so called exhaustion path. Tempt to do it with your computer ! Enter "I want to find a mysterious File". And now you may read the answer on your monitor... until some more millenaries.

Therefore, during millenaries, this circle (G) has produced an illusion of the magic of this axiom ! It is why the old Pi value is really an UNPRECISE value. And the Archimdean property is an ERROR when used to seek an unknown. We only paid homage to Archimedes to success to determined empirically his Pi value but we can not make this value as the base of modern technologies the consequences of that may be practical serious damages and we can not make this Archimedes' axiom as a big foundation for the modern mathematics.

The Archimedes' property is very used in all the mathematics...

The Archimedes' axiom or the Archimedes' property, may really produce illusions. The greatest illusion is that one believes that the Greater and less comparisons is equivalent to the Equality property. The order do not be considered as a number quantity, that is the ordinal and the cardinal may not be confused. Something that is classed as greater or less than is no more a number concept.

Now because of the concept greater and less are included in the Archimedes', this theorem may generate many other unknown confusions in mathematics. E.g. the Archimedes' is very used in Number Theory. We analysis a proof of this theorem that was found in a mathematics textbook for education.

This following example is taken from textbooks for the mathematical teaching that are very serious. Many mathematician teachers has read it. This means that the next demonstration is recognized as true and may remains as it for a long time. There are not reproaches for person. They have all the necessarily skill to teach mathematics. Therefore, the untrue of this following proof is useful to show us how millenary darkness may be attached imperceptibly in the modern thoughts.

A same confusion in reasoning like as that we can find above in the problem of the Pi resolution.

This is the statement of the Theorem denoted as the Archimedes' Property.

Let a,b belonging to N the natural number series. There exists a positive integer n such that n.a is greater or equate to b.

This is only an equivalent of the Archimedes' property witten above. Now follows the proof. In preamble, this theorem can be proven because any variable in the statement are defined. This is not the case if this theorem is written as this :

Let [a,unknown] belonging to N the natural number series. There exists a positive integer n such that n.a is greater or equate to [unknown]. In this form, one can see that this theorem is impracticable.

Now let us analysis the proof, that you can find the same in many serious education textbook. This is to prove that n.a is really greater than [b].

We suppose that the result is the inverse, that is to say that n.a is found less than [b] thus for any positive integer [n].

Consider the set S=[b-n.a] with n belonging to N. Thus, S belong to N an is not void.

Considering the order property in S, there is {s₀} belonging to S such that {s₀} < any [s] belonging to S.

Let be denoted {s₀}=[b-n.a}.

All this is defined normally to drive to the conclusion that if n.a is less than b, than one get a final contradiction. Thus, :

If b-(n₀+1)a belong to S, one must have

b-(n₀+1)a} >= b-n₀a

This means that

(n₀+1) =< n₀

Conclusion : therefore, it is obviously a contradiction.

This end the proof. Now this demonstration remains as like it during a long time and everybody agree to the true of this proof.

However, this proof is false. And this is the reason.

(n₀+1) =< n₀

Therefore is obviously a contradiction...

No ! There is no contradiction in these results. Because it is a logical result that

(n₀+1) <= n₀

must be written as

- (n₀+1) <= - [n₀}

... because the author of this proof have written a negation before these variables. Thus, their order are inverted ! The result of this proof is really as follows :

(n₀+1) >= n₀

... This means that the Archimedes' property is not proven there. In fact it is only this proof that is not correct. But it proves that there is a great confusion about the Archimedes' Property around the exhaustion, the Real Cuts, the convergence,... and mathematicians have still too much things to do for rebuilding what is wrong.

Behind the so-called Archimedes' Principle

- Archimedes + principle + validated

Tempting to validate the Archimedes' Principle shows that one is still misunderstanding the basic error of this principle.

The Archimedes' Principle cannot be validated ! Because a contradiction can never be validated.

One must see clearly what is false in this Archimedes' Axiom or Principe. Because this so-called principle is use as an exhaustion method to resolve an unknown datum.

1) - The exhaustion method is not a Principle. It is only a practical process.

2) - If there is something in this so-called principle that is a principle, it is the natural number recurrence.

What is the basic property of a recurrence ?
A recurrence happens when ALL members of a number series are known. For example, the natural number series is precisely determined in a whole with the recurrence principle. Consequently, a recurrence in a set of numbers means that there is NO UNKNOWN elemnt in this series.

Therefore, the so-called Archimedes' Principle is a wrong application of the recurrence principle.

Practically tell, let the natural number series. This is a series where the number succession 1, 2, 3, ... is generated by recurrence. Now, everybody can use the successive or the preceeding number generating method to exhaust the natural number series. All along this latter, one can not find an unknown one. This seems astonishing but it is the logic true.

And the trick in this use consists to prevail a practical exhaustion process by a recurence principle that masks the false reversing of a mathematic statement. This latter is the confusion of a Consequence - the exhaustion - with some Principle - the recurrence one.

Now, the real application problem of exhausting a number series, it is the not yet a resolved one. This problem is as follows :

The fundamental mathematic problem consists of applying the unkown data such that it can match with the number series pattern.

Here, it appears clearly that numbers are language and human has to match his language articulations to the "UNKNOWN" data in nature where he attemps to determine.

THIS IS the true and funcdamental problem, NEVER RESOLVED in mathematics. And nobody can still mask a such important problem when trying to validated the so-called Archimedes' Principle.

Remind that the Euclides's division is only an approximative practical method that tempt to find an unknown number that may fit with an element of the natural number series. In fact the result of this division method is never true !

Example:

- Physical + "Quanty" + of + physics (India)

Physical measurements generally are rounded...

- mathamatic + teaching + money

The quantities 1 penny, 2 pennies, 3 pennies, ect... are all known in all the natural series numbers. And if one says 1 billion of pennies, everybody knows its quantity according to the successive and preceeding process.

Now, in the pocket of somebody, there is some quantity of pennies. This quantity is also define in the natural number series. And as the Archimedes' principe tell it, there is always another body richer or poorer relative to this quantity ~~quanty~~. This is the true.

However, even if everybody may be richer or poorer relative to this quantity, if one make an exhaustion of the natural number series, this can not allow to determine what the preceding person may have really in his pocket.

Result:
The true of the natural numbers series property, can not be apply in practice to seek an unknown quantity, even if this latter is also an element of this series.
This is because out of a series number structure, an unknown datum can never be known. The numeral language consists of correlating unknown data to match with a known number series. What does it means to correlate it ? Simply, the correlation is done as follows. This person want to by a cake. Then in the store, he have to choose the cake price that is in correlation with the quantity in his pocket. At this time, the correlation is done between the natural number serie that represent the known price and the unknown in the pocket. Finally a precise correlation is need to know what is the quantity in the pocket. If the person does not like a cake, the correlation is done when at home, he count the number of pennies in his pocket. He says : one, two, three,... This is the precise correlation that matches the unknown pattern with the natural number series one, that allows to know. Without this counting, even himself, does not know what he has as amount of money.

An approximate manner to know the unknown is to situated it between two precisely defined value. In example, this person does not know himself what he owns yet as money. But deducing from what he had spend globally before and what he had the latter time, he can approximately suppose how wealthy he is. However, statistics and convergence methods are only approximation and give no means to have a precise quantity definition. And adding numerous decimal digits after a number does not means precision. In the contrary, it is harmful ways to introduce inconscious severe errors. One known it, mathematic is in fact only approximative methods since millenaries, from Euclide to Archimedes and modern Algebra. Introducing irrationnal numbers is a most great proof of mathematics failure.

Mathematics do not know a precise method. The Archimedes' Principle is only a severe belief.

A proof that the square root of 2 is a universal constant since the Beginning of the World

Give me the TWO...
and with the Square Root of TWO I will build The New World !

- the + photos + of + famous + costructions + in + the + world
- wher's+a+good+site+on+robots
- Mathematics Point Carre New proof
- constant + value + calculations
- associate + constant + dissociate + constant
- that's + proof
- eureuka
- marvellous dust

- WHER + THE + MATHEMATICAL + INVENTIONS (Vietnam)

...h'm... please, somewhere try with robotsearch... :-)

- proof that the square root 2 is irrationnal

These proofs are huge mathematics errors. I have given so many fundamental reasons for this. And many erroneous proofs don't mean equality with the truth. In the opposite, hereafter is a proof that Square Root of Two is a basic universal constant in the matter space.

So, I give here an another practical proof that can be get owing to the Dakhiometry method. Really the Dakhiometry is a marvellous one and one could not fall into errors with it.! Hereafter is a series of unlimited quotients where each element is exactly equal to square root of 2. Exactly, because the Dakhiometry manipulates only lengths in spatial figures. Thus, hereafter are this series construction where [sqr(-)] represent [square root of (-)] :

2¹ / sqr(2¹) = sqr(2)
2² / sqr(2³)
2³ / sqr(2⁵)
2⁴ / sqr(2⁷)
2⁵ / sqr(2⁹)
....

- Math + Properties + of + "Expoents" (Bahamas)

Too long too explain it... May be, a next time.

In this above series, one can note that the exponent are the natural number series. The denominator exponent is odd numbers and each is equal to the numerator exponent added to the preceding numerator one. With this rule, one can get directly to any term of this series, from any given numerator number even with Real numbers, as long as the difference between the two successive numerators is equal to the integer unity 1. This series is therefore for Real numbers.

With the Dakhiometry's figures it is straight that these exponents are the numbers of the discrete elemental matter da-khi that on tells it until now as the Real number series. Recurrently constructed, it is obvious that this series has the cardinal of N, the Natural Numbers, the one that counts the elemental matter da-khi. This series is written as :

2ⁿ / sqr(2^{(odd n)})

Each element of this series is exactly equal to square root of (2) ! You can see here a new curious series of quotients reveled by the Dakhiometry. This is an occurence for a steady proof of the impossibility of irrational numbers where the recurrence property is used.

- What + does + Pi + "equel"

Sorry, Pi is never equel to a polygon nor anything else, according to Archimedes' proof.

Result

The Fundamental result is :

1) - The irrationality is a severe contradiction to the Recurrence principle. The irrational or the Infinity that are a same erroneous idea is shown in the Zeno's Arrow and Achilles praradoxes where are concerned the motion phenomenon. And motion is the phenomenon of the Recurrence process of the discrete matter. Therefore, if the space is a Continuum of irrationality and infinity, then no Recurrence is possible. Consequently, no motion is allowed and never exists in the universe. It is why the Zeno's Arrow and the Achilles stan on the spot like in a nightmare as shown by Zeno.

The above Dakhiometry's series of number is starting with a number that is until now supposed as an irrational number. Therefore, if this irrational property is True, then the whole universe should be irrational. This number series can never be formed. Also, no number can exist because numbers are produced by the recurrence process. This means that nothing in tha universe can be known. No motion is there allowed. Therefore, nobody if any, can move even his tongue. Consequently, nobody can never said the world "irrationality". Therefore, this present issue is closed by an EEK... And the worst, nobody can never hear the silence !

2) - Any number in the universe is built with the value of the Constant Length Square Root of Two. Correspondingly, the universe built on the basis of a First Constant Length, in the meantime appointed as "square root of 2" !

If one examines this Dakhiometry series, you will see that any number, and more exactly, any length is determinable by means of this series, taking into account the exponents of its elements. More precisely tell, all Elementary Location of the universe is defined with this series that rests on the Constant Length value square root of 2 !

This series is of Real Continuum type. And since the matter is discreet, it describes what is OPTIMAL, PRECISE and JUST : the Completeness of Locations of the universe absolute space. The matter is dixcrete but the Succession process is the continuity of the Recurrence. Examining the odd value of the denominator exponents, the constant Succession in the space gap of the length Two is proved rationnally in Dakhiometry with "the Compass and straight edge". This concerns the gap of 2 between two odd numbers, that are here at the dominator exponents.

Importent note :
This number series is directly derivated from spatial figure constructions and non from definitions, hypothesis and axioms as in algebraic systems.

For example, consider the element hereafter :

2⁴ / sqr(2⁷)

We have 7 as the sum [4 + 3] = 7
The above series can be formed with numeral of the Real type as:

4.35 + 3.35 = 7.7 ; or,
4.832851 + 3.832851 = 8.665702
Finally we have the element as :

2^4.832851 / sqr(2^8.665702)

... and so on, with the condition that :
4. - 3. = 1

In summary, with [x} any decimal numeral and any sign of the numerator, the most simple form to define each element of this series is :

2^x / sqr(2^(2x-1))

In this element formula, the exponent [x] can variy from the negative to the positive both as endless values. This endless line is in fact a line starting from the dakhion elemental length denoted at the negative exponent value of 2, to the endless real universe dimension denoted by the positve exponent value.

Therefore, this series is well representative of the Universe Line containing the elemental lacation Succession in the whole space. This Line begins from the elemental ultimate da-khion, expressed as the most negative value of the [2] exponent. Then, this Line starts growing toward the unbounded great value.

- immutability + immortality + proof

The complete definition of this Equation Generator of numeral series... please CLICK herafter : The Equation of numeral language...

Fundamental Corollaries

The number series 2^x / sqr(2^(2x-1)) proves that :

1) - The (square root of two) is a spatial universal Constante. It value is precisely determined.
2) - The universe space is an absolute rational. In anywhere of the matter there is no fault communicating with a beyond.
3) - The Infinite is an erronneous concept, according to the following equality :

2^(infinite) / sqr(2^(infinite)) = (square root of two)

4) - In the opposite of the Infinite that means Non-Being and Nothingness, this series prouve that Constructions in the universe is DEFINED but nevertheless, it is Endless.

Take any decimal value for [x] that you want for the exponents as tiny long wide or huge as you like it. Also, the sign of the element depend to the numerator sign that may be +2 or -2. However, don't throw avay your calculator when tempting to compute any element of this series while stubbornly as an obsessive catchy tune the calculator answering is ever the same square root of 2 value. Be magnanimous with your calculator that is not even so always stupid. Because this value is the precise particularity of this series that tempts to told you simply that the matter space founded its first construction stone with the help of the length equal to the square root of two.

This series is thus a continuation of Succession, defining the complete real Line composed of all the elemental discrete matter in a given Direction of the space.
The definition of numerals in the interval from Zero to Two is made with simple spacial constructions that are real length quotients.

This unbroken series of producing numerals is the proof that the irrational square root of two is no more than a severe error that for mathematics should be an emergency of checking and correcting.

Therefore, the continuity of length is no more than the rational elementary location succession of the space. It is what is celled until now as the erroneous Real Continuum. Therefore, a new process of numeral determination can be done according to this method to replace the Real irrational and trancendent holes.

The above pjysic of the matter space is erroneously know as the Continuum of the Real Line. And the errors of the Real numbers constructions with that one is convinced to "prove" the irrationality of numbers, was only artefacts of the Cut and the Convergence errors in the Real Line that rest on a Archimedes' Principle. This last is only a void principle.

The Archimedes' property is a trompe l'oeil...
This principle is void because it is a trompe l'oeil where everybody is falling into a trap. I had shown it with the analysis of the attempt to determine the Pi value with the polygon convergence method. This principle is unusable because with the More-than and the Lest-than method no precise mesure is possible ! In the ancient time the inequalities are used because at this time there had no means for a more complete precise conscience. In example, the Ptolemy's quadrilateral theorem used an inequality as a last resort et non as a divine law. In Dakhiometry, this quadrilateral theorem is proved and expressed as precise equalities. And precisely, the Convergence was established in the Hilbert's Axiomatic from there one BIELIVES that a convergence allows to catch any unknown value. This method is not rational even so when some gods and dinosaures was invoked as Deities attached to this method...

May be, one can catch a flying balloon using the convergence of his two hands. But with this pocess one couldn't get everything... and wants to have his cake and eat it even if he is a great champion. Therefore the Archimees' property yields necessarily some unpredictable artifacts..

- simple + "explianation" + how + to + measure + vacuum

For current ultra-vacuum that is lower than
1.333^-6 Pascal and no more lower than 1.333^-10 Pascal, a Pirelli gauge is used. It consist to ionize the atoms in the meeasured vacuum between a high voltage of about 350 Volts and then to measure the current of the ionized gas. This current is proportional to the number of atoms remaning in this vacuum. However there are some atoms of rare gas that are difficult to ionize, thus this gauge is not always an exact vacuum measurement system.

- explanation of + ADC + successive + approximation

A.D.C. is the electronic system wide used to convert analogix signals to digital ones. This is technical method widely used and the principle of that is to control an action using a feed back process to maintain an action of the system compared to a reference level. This last function of comparison gas something to do like the Convergence according to a like Archimedes' property law.

These techniques are very efficient. The most simple one is e.g. the air conditioner that allows eveybody to regulated the temperature of a room to a determined reference level choosed by himself. What is concerned the Archimedes' property is that the regulation is done by the system to adjust the room temperature to the reference choosen. And this is done nearly as Archimedes had do it when he try to calculate the circle perimeter in doing the convergence of two polygones toward an ~~hypithetical~~ hypothetical perimeter of a circle. - "hypithetical" + anti + grav (USA navy mil)

- work + "remperature" + conditions + law (UK)

Do not care to a temporary work hypothesis... - "hypithetical" + model (USA)

However, the success of the regulation technology should not be the one of the Archimedes' property that is the stumbling block of the Algebraic Convergence method used for Reals number and many other process of function convergence. Why is it so ? I have shown it during analysis of the Archimedes' Pi calculation. In summary, it can be tell as following.

1 - The technology process has a high efficiency. It is because it has only to compare and adjust TWO perfectly DEFINED LEVEL VALUEs. Only a feed back measured and determined signal has to compared to a reference also determined signal.

2 - the Archimedes's property and its use by Hilbert in Algebraic axioms, is exactly an erroneous method that rest of a dummy principe. Because in the Archimedes' polygons and in the Convergence algebraic method, the proces is to Converge a comparison system, toward an UNKNOWN variable. That is in the algebraic Convergence process, the principle is to use this system to detect an unknown object. The unknown objects are e.g. the polygon perimeter convergence toward the circle perimeter, irrational and trancendent cuts. While in the ADC, anything is perfectly defined. The convergence system is used to compare a GIVEN measured signal to a GIVEN reference one.

Warning !

This are the secret of the erroneous Archimedes' property application. Because this principle is only very fine to manipulate only DEFINED values. Therefore, this science condition should be applyed to any statistical method that couldn't give other things than a gap of prediction results and never a precise value even with large samples. This is why since the statistical sciences was established, the idea of Heisenberg' Uncertainty appears. And in its subatomic scale, statistical methods should give necsseary many impredicable erronneous interpretations.

Why Heisenberg Principle is not a Discrete Mechanics

- Heisenberg ++ conservation + of + action (USA)

From the Planck's constant (h) taken as an action element A.
As A=m.v.dl, its Equation of Dimension is given as M.L²T^-1.
Conservation of Action is really a basic Principle. Now a conservation of a constant, means that A is necessarry an immutable form. If this condition is not stricly verified then there is an error in this datum of a so-called Action.

In the following, what happened with the Quantum Machanics about the Heisenberg Principe? It was to take the Dimension Equation of an Action to write it as an analytic equation. Thus the constant (h) is witten as:

h = (m.l.l)/t

In this way of formalism, the Quantum Mechanics stands on a big contradiction against its Conservation of Action Principle.
Because with a such formalism, there is three big contradictions:
1) - (h) is then an hyperbolic function and is no more a Constant. It is a mind disoder of formalism, to state that in y=(1/x), the (y) is there a constant.
2) - This formalism means directly that (h) is not a Quantum. Then the contradiction is why Quantum physicians applied its as a Continuum formalism. For example, {m, l, t} are taken there as Real Numbers.
3) - The fundamental contradiction is there to do not understand the corollary of the Action Conservation is directly the Conservation of Energy.

From there, we know why Worm holes are created with a such confused mathematic formalism when the time (t) is infinitly going toward zero and why from a practically nothingness (h), physicians create Infinite energy of virtual holes.

Or, all the numbers are irrational or, there is no irrational one !!! Because the recurrence principe implies that the property of the first elemnt must be reproduced in the whole series. According to that, the Real Line is thus composed of irrational holes therefore, and no Continuum is possible. And precisely, the contradiction is that this Continuum is the foundation of this theory.

Consequently, It is clear that something should be wrong in the irrational world since the famous incommensurable diagonal with the square sides. The conclusion is : no irrational number is possible and the Square Root of Two is only a basic universal length for the space construction. This why as long as the irrational dogma remains, there couldn't be any steady science. And sciences are only hypthesing systems. One know that with many IF, everyone can buit his own world. This why the current sciences is so prolix in producin not of imaginativeness creations but too much with imaginings of astonishing dogmatic worlds.

What should be retained is that :
The Square Root of Two is a PROOF that the Irrational is a severe ERROR of the thinking.

What is the Archimedes' principle ?

- Archimedes + used + inscribed + and + circumscribed + polygons + to + approximate + the + area + of + what + type + of + figure (USA)

Probably, Achimedes had tried to use the method of dividing any both straigth and curclinear lengths to try surimposing them, according to the Euclide statement that equality is the exact superposition of two lengths.

However, it is a Fact that curve and straigth lines can't be superimposed together. The more, it is a real logical contradiction to believe to this possibility.

1) - Straigth lines and curves can't be supperimposed directly. The impossibility of Squaring a circle proved that.
2) - Polygons also, can't be measured with the Archimedes' method of convergence by two other inscribed and circumscrobed polygons. The proof of this is shown by the difficulty of mathematics to do the angle trisection.

Because converging toward a given polygon by an another polygon, need not onbly dividing in straigth infinitesimal segments but more basically, one must know how to divide angle!

- archimedean + principles + property + unbounded

The Archimedes's Principle can be stated as follows :
In the space, e.g. a line, an aera and more generally in a KNOWN exhaution domain, one can converge toward a KNOWN location, proceding by any approch means particularly with convergence movement toward this KNOWN location. The result is inevitably and necessarry the reaching of this location point.

This Principle is a permanent Fact in the nature.

Application :
DETERMINE a search domain e.g. a line. Now, choose a point on this line. This point is thus KNOWN. Apply the above Archimedes' principle. Then, in a KNOWN domain line with a KNOWN point on this line, everything can reach this point. This always runs well. This law is never missing. It is why many men of genious has adopted this principle as method of searching something.

- physics + sponge + archimede

- tautology + highest + top

- discreet mathematics tautology free + downloads

(Really and truly you said it !)

- Resume + how + they + should + look + like + when + applaying + for + a + job

NOTE:
All what follow are not against Archimedes. If this is not himself the initiator of these games you can be sure that it is with him that we are laughing.

Example of Scientist persevering in Application Research test :
- mathamatic

- discribe + a + monks + daily + life + during + the + middle + ages

- how + can + Archimedes + Principle + be + used + in + real + world + applications

- archimedes + principe (Germany, Universität Mannheim)

- Archimedes und pi (Germany, Berlin Offnes Deutches Schul-Netz)

- controlled + and + convergent + approximation + for + exhausting + the + circle + by + polygons (Canada, Québec, Montréal University MacGILL)

Convergence method proves that man is very ingenious. However, the human science aim is to be in precise consciousness of the world. And convergence prove that fishes can be caught in a net even if one don't know precisely where they are. Fishing net shows that convergence can give results in practise. But there is some weird things proving that Convergence Technique is not a precise, accurate and controlled catching everything tool.
For example here is an endurance trial of convergence method in the human History. We see here a Straight Polygon trying to catch in the fly a nice Unknown and Round Circle...

- archimedian property? (USA, California State University SAN BERNARDINO)

... actually, a test according to known principle.

- Archimedes half + way + to + wall (USA, Chromosomal Laboratories, Inc)

Fon't touch ma Question:
- how + many + iterations + did + it + take + Archimedes + to + reach + 5 + decimal + places ? (Canada)

Answer:
- converge + toward + never + touch (UK)

As long as he needs it.
But, there is some problem of the W.Y.S.E.W.Y.G technology to resolve...

- Archimedes + tortoise (USA, Michigan Technology University)

- The + archimdean + property + of + real + numbers (Namibia)

- POUSSE + D'ARCHIMEDE (Russian) Federation)

- Archimedes + (did + he + do + anything + bad)? (Canada)

Yes he did. Because may be, he also catched a cold when running naked while shouting Eureka...

- example + de + diplôme + de + grimace

- famous uses of pi

- practical uses pi

- Archimedes + modern + influences

- what + the + tortoise + said + to + Achilles ?

- real + world + application + of + Archimedes

- tickle + tortue

- uses + of + third + law + of + motion + in + real + life + situation

- How long did it take for Archimedes to discover pi

... he was still a young man...

- Archimedes + + measurement + of + infinity

- example + of + archimedean + property + of + real + numbers

- application + of + archimedes + principle + in + everyday + life

- Irrational + roots + located + by + the + Location + Principle

- Archimedes + analysis

- Full + definition + of + the + Archimedes + rule

- one-one + correspondence + archimedes

- understanding + green + strokes + theorem

- Archimedes + square + root

- what + does + archimedean + property + mean + really ?

- Archimedes + and + the + tortoise
- iteration + calmos
- Archimedes' + thrust
- Archimedes' + missing + work - is + archimedes + principle + used + in + present + day ?

Note : What. You. See. What. You. Get.

- Definition + of + an + Intellectual joke

A step of a circle understanding is actually done...
HUMAN IS EVOLVING

There is the fact that a step in human mind progress is realized as following :

- Why + a + circle ++ not + a + polygon

We have there a remark that should be taught in mathematics and also in every sciences.

Since before Archimedes epoch until now, HUMAN DON'T UNDERSTAND what is Circle, what is the Round. Therfore, if Archimedes had fail to access to the cercle measurements according to a polygonal mechanisms, it is not because he was not competent, in the contrary. We must see there a proof that TODAY human was staying in a certain upper level of mind development. And the above remark is a new realized conscience that must be transmitted to all the Earth mind : HUMAN is ACTUALLY EVOLVING. He is surpassing and now getting to a new level of evolution.

Be carrefull please to do not lose the meaning of what I tempt to tell.
Why are we reaching a new level in mind development ? The reason are as following :

Because the universe is round - :-) - and is really a physical Permanence then, an Existence Beginning was allowed. And it is proved in this site that Existence Beginning was done from transmuttation of matter that allows producing multiplicity of Forms. The squaring from circular state of matter is the fact of this universe step. Therefore, "the universe is round" is the permanent universe property. This proves that fundamentally, :

1) - Matter is symmetry.
2) - Circle is permanent matter symmetry structure, then : CIRCLE IS NOT A FORM.
3) - Because circular structure is Permanent and is Anterior to the Beginning, the Forms that are posterior to the Beginning can never be compared mechanically to any form Anterior that do not yet exist. Therefore, a POLYGON CAN NEVER BE MECHANICALLY EQUALLED TO A CIRCLE that fundamentally is not a form. This is a matter property even if surface and perimeter of circles can be exactly measured and compared as quantities. Then the squaring a circle can only be done indirectly through quantities relationships.

According to these view point, Archimedes' works is a SUCCESS when considering that he had proved the real physical impossibility of the above equality !

There is then some matter properties classes that can not be compared together. Consequently for examples, the ZERO that is a language convention can never be compared and confused to a QUANTITY that numbers represent. Also, the UNKNOWN data, can not be compared to quantiy in a relationship when one used to write Inequality Formula. Inequalities are then only qualitative relationships.

For me, human have to be glad of his Understanding that POLYGON IS NOT CIRCLE because it is really a great human event after wandering through so long millenaries knowledge adventures. Because human knowledge is now enlighted by the fact of the Before The Beginning matter state !

- who + are + the + mathematicians + Cantor + and + boule (UK)

A mathematicien may tell in French: "J'ai la boule". May be, everyone needs not being Cantor to complain so.

- archimedes + cantor + completeness (United Arab Emirates)

- solution + for + Use + the + Archimedean + understanding + to + prove + that + a + series + cannot + have + more + than + one + value.

- What + is + the + Archimedean + understanding + of + the + infinite + series + Show + that + if + this + series + has + a + value + then + it + must + be + at + least + 1.

- Archimedean + property + proved + cantor + not + axiom

- 12 + sided + figures + inscribed + and + circumscribed + in + a + circle + Archimedes' + approximating + pi

Dummy Principle There, Figure of an Impossibility

This is what Archimedes had done for searching the circle perimeter. It is to use the convergence of two polygons [pi and pe] having the diagonal equal to the diameter of a circle [C]. He thinks that the polygon convergence cannot but be directly confused with themselves and that at this point the perimeter of a circle [C] should be found. According to the above Archimedes' principle, the Domain of search is KNOWN. It is the two polygons plus the circle. And this circle is also KNOWN because a diameter {D] always define exacrly a circle. Therefore, there is no problem, the Archimedes' principle is wholy respected. Let's go for the Pi determination !

It is what everybody BELIEVEs, since Archimedes until know for the the Modern Algebra methods, include first Hilbert, Cantor, Dedekind and many other modern algebra inventors of the last centuries.

Unhappyly, the above Archimedes' Principle is not respected. Exactly this principle is denyed first by Archimedes and in the ful rcurrence by the other successively. According to the principle, one must have two KNOWN data that finally allows the possibility of the successful convergence. In the above Archimedes' manipulation, there is only ONE KNOWN datum. It is the polygones and circle domain. The circle is not there the known target. It is only the domain that define the diagonal [D] because a diameter only can't never defines a circle perimeter. It shohuld be underlined that one NEED NOT the circle representation. The two polygons suffice to define the domain.

Therefore, there is only ONE datum in this problem that dosn't allows any resolution. This circle is not a second valid datum. It appears that this circle representation is a dummy data that makes anyone convinced that this method is a really efficient one.

- what + are + the + archimedean + unknown + figures

- why + the + value + of + pi + lies + between + the + areas + of + two + polygons

Initially Archimedes' purpose was to find the circonference or the diaeeter of a circle that give Pi with the perimeter formula. Then it seems obvious that a polygon perimeter with a high number of sides should be confused to the circonference. In this case one polygon is sufficient for a solution. But, mathematical resolution is not so simple. Therefore, Archimedes tempted empirical measures with a polygon of a low number of sides. To reduce practical errors he had to uses to polygons to get an idea of the measurement tolerance.

This means that the found data should lie two times... if one believes that the circle is lying between two polygons.
With one polygon only one lie and obviously, the best is no lying polygon. In Brief, using two polygons means a quite empirical method and never with mathematic reasonning one.

- "matematics" + making + a + factor + triangle

- what + factor + determines + the + maximum + speed + of + logic + gates (Saudi Arabia)

Speed of changing state of an electronic logic gate is also an exhaustion, a real one. The exhaustion consists here of the changing states duration of the gate low-high. Its speed is then determined by the linear motion of its potential. Generally, the raising time is the one that from low to the high positions the time is linear versus voltage or current. These limite is defined as a percent of the defined low-high span. It is a process of exhaustion. The digital system work well as it is shown by computers.
The difference between real exhaustion physical processes an the axiomatic exhaustion process of Archimedes' axiom, is that in the digital logic gates, the two extrema of the exhaustion is known and perfectly determined. It is not the case for Archimedes and Hilbert's axiom where the unknown is quite unknown. And thus, because this unknown is not known, then, the two extrema of the exhaustion are also unknown or undetermined. In brief, with three unknown objects a 4th unkown one can not be determined even with the help of inifity convergence that is itself an another unknown.

- absolute + infinity + is + nothingness (USA)

A quite exact and precise definition of this Nothing that is a false concept! There is only the real infinity that is only the unbounded and unlimited reallity e.g. particularly the human thinking.

In summary, in the above figure, you should throw away the circle [C] and also one of the polygons. It remains only one polygon necsssary to tempt a resolution of the inknown circular perimeter.
In comparison, in the Zeno's Achilles paradox, you can also let undisturbed a poor tortoise that is not necessarily for the problem analysis. Consequently, you get now a clear correspondence between the two paradoxes : Achilles is no other given datum than the polygon with a constant diagonal [D]. Then the solution of these equivalent paradoxes, is given by Zeno. It is to tell that : As long as one has no goal, e.g. the precise perimeter datum and the precise position of the Tortoise, one never get the solution in hesitatingly go on by half steps. Because in mathematixs when concerning the reason of the thinking, getting only the half way in equivalent to add a negative motion, the doubt one, and means exactly to add backward movement to the positive one that is the convinced part. Therfore, you may go forward infinitly but the negative part of the total motion is also growing infinitly. Thus, the more you go on the more you go backward this is why you couldn't but staying on the spot ! This is the rational solution of the Zeno's paradoxes. This equation is deduced directly from the Conservation of Action principle. The action and the negation of action are not accomplished actions and therefore, they remains conserved in body system as parasites and interferences effects as for example, a tense muscle end in cramp.

Consequences :

The mechanism of certainty and uncertainty antagonism affects the whole life behavior. Thus, when one is acting with in the mind a part of uncertainty, he knows a growing of the action negation inside him. This latter constitutes an psychologic reservoir of action negations that grows with experiences in time. This is the part of the anti-action of the doubt that remains in spite of desappearring with experiences.

What are these mechanisms in sciences ? It is undeniable that the uncertainty in sciences had known the same effect of action negation. And it is not surprising that sciences go more and more to abnormal complications that are the visible aspects of the anti-action of the uncertainty. The Relativity an its alter ego the Quantum Mechanics, are the phenomena of these mechanism influences. Because they rest on uncertainty of the Past. In modern time, sciences are only the probable sciences of probability methods.

It is no need to emphasize on the huge gasworks of modern societies... But it is far to be an inescapable way if the modern life. It belong to the humain mind to rebuild his knowledge justly founded and everything with goes in its optimal, just and simple in the wealthy way of life.

One can now expressed the Archimedes' Property as a questionning :

- "What is true but is not true"
- "What lies but is not a liar"

Apparatus for seeking lost objects

from...

- invention + unknown + variable + algebra

The Archimedes' property resumed in the Hilbert's axiom with wich Dedekind builds his Real Numbers Line does not tell anything more than this figure shows.

In an area, here is as segment [AN] on a line, one can sweep the line with a cursor [M], starting from [A]. This cursor finishes always by exceeding any point [B] of distance |AB]. This is the famous Hilbert's axiom.

You can now create a manufacturer that produces and sells an apparatus for seeking lost objects ass the Vacuum salesman had do it one day when he applied the Einstein's Void Obviuosness. Looking at this figure, anybody says OK to buy the Seeking Lost Object apparatus.

Now, affter the purchase was done, you hope to find with its some lost housekeys. On the figure, the salesman had tell that at the Known point [B] should placed the Unknown lost object. Then, it suffices to move the cursor [M], on right and left, to meet the Know point [B] of the Unknown Lost Object. OK fine, let us go for finding again my lost Keys... But wasting days in moving the cursor, you are enable to find again your precious house keys and is yet staying outside youe sweet home. You are still thinking about the mathematic diagram of the apparatus : well, he says that my Unkown lost house keys should be at the place of this Known point [B] ???... But something may be wrong in this explanation because my Lost Keys... I KNOW its. So, my know Lost Keys, should be placed at the knows point [B]... Therefore, try and error is a good process.... but until now, you are sleeping in the open...and are missing tbe be not a great mathematicien in the younger days.

This is an aduous problem... is my house keys a Unknown even though they was my usual familiar house keys ? Why this point [B] is unknown while obviously it is well known on this figure ??? How mathematicians do to find unknown numbers |B] when with my known keys, I can't find it again??? Am I so stupid ??? If my keys are unknown and I put it at the place of point |B] then, how can I do to know that the cursor [M] is at left or at right of it... because in this case, I know where they are... and if I know where they are,... obviously... I don't loss my keys ??? ... Please... Help ! After that, I promise to take care of mys keys in the futur...

The Einstein's Void Box...

or, how a reasonning error set up the never mentionned Void Principe that control any scientific theory

The mechanism of seeking a lost object is a harmful of the human thinking where he is trapped by the obviousness of imageries that fill in his thought.

In this view point, Einstein wrote himself that he do not agree with the Descartes' Non-Void. And in the coninuation, he can conceive an ideal box where any matter can be take away and thus, there is only the Void or the no-matter. That is the box of Nothingness.

This definition of Einstein's reality shows that nobody is immunized against commonplaces. Because the statement of the obvious can tell that "a box is a box because it contains". However, in this case the true is really absolute because a box necessarry contains. It contains anything include the "nothing" of the everyday. And because it is the realty, it couldn't contains the Void of the world or the Non-Being, the Nothingnesse. Because in this case, the Reason Goddess does in such manner that both the one swallows the other not to beach about the bush.

The main key of the error is hereafter,

Proof that the NON-BEING is a fatal contradiction to the BEING

The deep error of the Void Box stands in the obviousness of the human habit. This make everybody confuses the though Contradiction with the reality of the Complementarity in life.

1) - The complementary says that "a box contains". Therefore, what is in the box exists really as well as the box. Result : the Nothingness exists naturally in a box. This conclusion is the result of the obviousness of the common idea that a box is a container and thus, the Void is obvious because it is qualified as a content.
2) - The Logic Contradiction says that the Being cannot be both a Being plus a Non-Being. Example, the Void of the Nothingness can't stand aside the Being of the matter. There are two reasons for this :

a) - Because the Ex-istence denotes the fact of Going-Out-From-Being,
the BEING is a necessarily and sufficient condition to produce the Existence.

b) - Because it is known as the oposite of th BEING
the Non-Being is not a necessarily nor a sufficient condition to produce any Existence. Therefore, the Non-Being is a "whole" Nothingness that does not suffer any contradiction due to any presence of a Being.

Therefore shut up by Einstein, the Non-being standing beside a Being is contradictory to this latter initial statement because a such non-Being is a non Existence. Then, an Einstein's Box that can't contain is not a Box!

Also, the Non-Being shut op in Einstein's Box, that has therefore a Being Box around it is also a self contradiction, because the continuous chattering Being says "Pick-a-boo! Here I am aside you who claim ever find nothing but Nothingness".

Conclusion:
The obviousness of the simultaneity of complementary existence have induced an error in the Einstein's thinking that allowss him to confuse and valids a legitimacy between the Non-Being Nothingness that stands as the obviousness contain of a everyday box. While the foundamental logic contradiction should shows to him that the Being of a Box can never touch the Nothingness in a fair neighborliness.

Unhappily great, great contradiction in Quantum Mechanics foundaation...

The result is that a material reallity of a bax cannot be use to shut the Nothingness up. In consequence, there is no Void of the Nothingness. But in alternate manner, if there is No-Void, then a Ful Of Matter Principle should be necessarry defined by any scientific theorist. This was not the cases for the Einstein Relativity and also for The Quantum Mechanics. Both are born during a dark epoch of a murky period of the world history. The Quantum Mechanics supposes a world floatting in the huge Void where particles and wawes are wandering anywhere. The Void of the Nothingness should not have something to do with the quantum concept ! On can prove that the Void of Nothingness is a Continuum concept and the Continuum is the Infinity of the Nothingness ! So, tell me what a defined quantum has to do in a indefined world of the Continuum ??? What can you define even one point, in the Continuum ??? In consequence, the Big-Bang and the Expanding universe are examples of such productions. Really, the Void is a convenience tool easy to theorize anything.

- - explanation + of + gravity ++ wawes

Who can tell me where are these Great Powerful Sciences else than the one of Force Power of violence in techniques ???

It is with such dichotomic contradiction foundation that unconsciously Einstein had buit a hugue success for his relativity theory.

Stating that a box can shut the void up is to despise the Ancient Thinkers that have through centuries to struggle against how a Being and a Non-Being can cohabit. That is to say that it is useless to worry about such issue : I will shut the Non-Being up in my Big Box, the more are the Nothingness, the more I have a Big Box...

In this anti-principle Einstein had swept in through and founded his science. From this masterpiece of Void grow modern science schools where the universe is nothing than a huge Void in which stand some random mass, swimming through informal energy Fields that can appear in random by the will of the scientists. theses sciences manufacture their languages that are nomore than formalisms to create imageries.

No for a such world. Because the human knowledge, the one of each, is necessarry simple, peaceful, precise, optimal, Just and marvellously wealthy for life. Knowledge is Goodness of what is Being. This is simply to tell, it is the precise consciousness of the Now-and-There that form the universal science for each.

...

- invisible + form + which + transforms + itself + into + visible + form + as + matter

... this a realistic physical view point. Because visible and invisible are in the scope of complete matter properties. Like radiation phenomena, there are a large unvisible domains of non-contact with human scale which obey to matter laws and non to random behavior. These invisible matter states is denoted as the universe Breath or the dakhi gas of ultimate elemental matters the knowledge of which is fundamental.

The Dakhiometry is
a knowledge of the Full-Matter universe !

The universe is wholy full of ultimate matter elements of the Breath. This last is physically designated as the da-khi gas. The knowledge of life that is the universe's one concernes the science of this matter. Life is the consciousness that allows precise relationships. The Dakhiometry constitutes means for this purpose. The general knowledge on the da-khi is a goal for the Da-Khi-Hoc traduced as the Dakhilogy, a new precise science on this matter which is both the substence and the essence of life.

The Da-Khi-Hoc is thus a study on a universe full of matter da-khi, the discrete matter that appears in two aspects in Space and in Motion. Here, the knowledge should cover over

a Full-Matter universe.

One can not be confused in takeover of the Da-Khi-Hoc by current sciences. There is a great reason for not doing that. The Da-Khi-Hoc is not getting involved in immaginaries of the Non-Being, the Nothngness of the Void and the multiplicity of Infinities of the Continuum in that the current sciences remain trapped by multiplicity contradictions. One can reject the Da-Khi-Hoc as like it but don't make a mixture of this new science with the Relativities, tha Quantum Mechanics and the past sciences. The contardiction are then too visible.

Aristotle had tell that the nature abhores a vacuum. However theNothingness of a Vacuum remains tenacious as a big WALL in the mind of everyone. The Einstein's Box is there a huge example of mistake. The reason is that one can't escape himself an invisible jail of the Obviousness. The scientists don't know how to conceive the physic of a full of matter. Don't tell : what's a full of matter when I can't touch it ? The answer is a simple one : the thinking is a real human sense ! The thinking tactil is even the Reasons. If eachone can throw away the abstract entity Spirit he can then see the human thinking appearing in its reality as a material process the alphabets of which is the reasons. In summary, if you don't remark it throught all the texts of this site then, I will emphasize it as follow :

Fot the Da-khi-Hoc,

The universe id a PLENITUDE of Matter.

See New proof of Refraction and Reflection laws that are consequences of the dakhi fullness in the universe. Please Click here :
Refraction et Reflection, physic laws...

- what + is + the + meaning + of + history

Conclusion :
The Archimedes' Principe may be clearly and precisely stated as follows :
1) - In a KNOWN spatial domain where a KNOWN point [P] is located, it is perfectly USELESS to seek this point as long as it is KNOWN.
Inversely :
2) - If a point OR a domain is unknown, it is also USELESS to launch a search after them because the problem remains uncomplete..

Conclusion :
The convergence applyed in technics are good processes because they use KNOWN data. While for any algebraic ones, and also for statistics that also tempt to converge data toward a probable known one, the above analysis of Archimedes' Pi determination show that one gets there only dummy results. The modern Algebra is therefore a too weak method because one is waiting to find there a rigorous mathematic.

Practically, this Principle says only that it is necessarry to have at least TWO DATA to define a third one. This is why the universe had begun to construct when the number TWO start from its ROOT. At this condition from the starting Constant Root of two, the universe can grow successively to define life construction.

The Precedence of Reasons in the Thinking constructions

The thought proceeds with construction of reasons and the reasons are not elemnts that are used in desorder. Else, the thought are heaps of unconstructed reasons with no constructed forms that can give some signification. One can find these construction examples, in the structure of any language.

Consider now the Circle Theorem xhere only are used Distances and Directions of space. They are uniqueness definitions. Out of the symmetry, the Directions can be precisely defined in a 90 degres quadrant. In this reference, the square root of two, a constant, is characterised by an 45th degree angle. Thus, this Constant is not defined by a square. This latter is comming in the existence posterior to many other steps of the successive reason constructions. The anterior steps are the birth of axial symmetry from what the Perpendicularity was established and consequently a squaring of circle can be performed at the end of these steps. This is the beginning of the rational measurements in the universe where constructions started. Therefore, it is really the Square that wears the characteristic of the Constant square root of two rather the inverse. The inverse is NEVER possible because the Evolution process never come back in close loop according to the Uniqueness Principe.

This is the precise explanation of the rational universe where is only Knowledge of Life. There is no exterior-of-life as well as no exterior-of-the universe. Then, the Beliefs is not exterior of the living facts but they are IGNORANCES of the Life Realty.

Now, I can say to you...

To whom that are set on harming to maintain the Irrationality dogma in proving the irrationality of numerals : you are sprinklers who get yourselves soaking wet ! You are standing in the non-fulfilment system that turns you over and over like a caged bird.

- pythagoras + we + yous + it + for (Norway)

May be, Yous is used as some another unknown incommensurate irrational number...

- everything + about + sine Ccosine tangeant

The space is really wholy described as like that.
But the Trigonometry is very reduced and poor as tool system because it is an additional meam to describe only angles. Space is fully complete when are concerned Distance and Direction. Distance and Direction are the basis of figures. Therefore, the Theorem of the Circle concerns the whole space and not the alone angle. Means to understand space are thus the Length Quotient with their complete meaning when determined by a circle and derivated other figure structures. As shown by this Circle Theorem, there is no holes in the Quotient of lengths, even with the discrete matter where the Discretness considered as holes of Nothingness is a severe error of the old standard thinking that was worrying about some World-Beyond and thus had generated irrational and transcendental number believes.

- if + cosine + is + not + rational + path + is + not + repeated

This a fundamental reason and you are right. Rational means unique and unique means discrete and discretness means possibilitity of location changes. While irrational means undefined quantities, undefined location of the continuum principe. Then, as like for the Zeno's arrow, no displacement can happen, no recurrent phenomena, therefore, no repeated path. Also, there should be no movement, no dimension and no point. Because even for a point, it is an elemental dimension !

Conclusion : irrational means nothingness and nothingness means no-meaning. Thus,... basically, in an irrational world you couldn't say thing like that even the word irrational.

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.

Calculations of the Pi value (oct, 2002) Geometrical determination of the new Pi value.

Proof of the Thales and Pythagoras' theorems (oct, 2002) Basic properties of Matter give means for the proof of the Thales property and the Pythagoras' theorem.

Proof of a general triangle model theorem (oct, 2002) The natural model of the Falling Body and the proof of a general object model with any triangle.

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 areas 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. Fulness is necessarry to allow Quantity. Quantity is Reality of the World existence.

More detailed analysis written in french only:
Succession and Quantity analysis.

To read more aspects on this theory, texts archived : CLICK HERE

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Merci de votre visite

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The Archimedes' Property

Analysis of the unfeasible of the Archimedes' axiom to resolve a problem. Nguyên Tân Tài