1 - This is the square that may be transformed into a circle, according to the surface conservation.

Warning:
"From this paragraph, the proposed constructions are voluntarily erroneous..."


- jokes about pi (USA)

In fact, the above transformation of a square into a circle is no other thing than the direct transformation of a circle into a square. Because logically, the squaring a circle is really the origin of anything in the universe. And logically, anything e.g. a square, can't create its own origin.
This is why until now, the squaring a circle is a dead end wall for Mathematics resolution according to that Mathematics methods consists only to confuse a consequence with its root. For example the Achimedes' polygonal exhaustion is to take a line of polygon to create a curve. Note that a square is also a polygon.

The circle transmutation is necessary the beginning, the unique one of the universe measuring conscience.



This is to show that the key for a squaring the circle, is unique in the universe. It is why this key give raise to the unique Space Constant that allows the universe construction.

To resolve the reciprocal of the squaring a circle, one must beging by the direct squaring any circle!

For this purpose, one must determine the "little circle" denoted as (C1) in the preceding proof. C1 is given only by a circle-square structure. Then from any of this structure, one have to perform the squaring the circle.

Then, with this result, one get the necessarry elements for transforming the given square into a circle of the same aera.

If you are interested on the reciprocal proof, please see the text written only in French:
The True reciprocal of the squaring a circle (Only in French)

Consequently,
Those who assert that he had resolve the Square into Circle transformation get necessarily true false solution!

It is because nobody can't do this reciprocal problem without succeeding resolving first, the direct Squaring a Circle transform.

- at the corner of the square (cndata.com, China) Four corners of a square is the four cardinal points of the Earth where everybody is refered to... :-) - how to draw an impossible square (wescodist.com, USA) - can + you + square + the + circle + of + te + inverse + sguare (Philipinnes) - how to draw alchemy circles (prod-infinitum.com.mx, Mexico)
	2 - Let be the diagonals of the square. Draw a first circle at one corner of the square. The ray of this circle is equal to the half of the square edge.

- squaring + the + circle + Anaxagoras (USA)

3 - Draw a second circle at the center of the square and tangent to the first circle.

4 - From one corner of the square, draw a line inscribed in the square and tangent to the second circle.

- the + universe + is + not + random (USA)

- transmutation circle (cdi.no, Telenor, Norway)

- tangent point (Japan, Mitsui Zosen S.R. Inc)

It is the point defined by this form structure for the immutable Angle Constant of tansforming circle to square and inversely.

- center Reciprocal (USA, Connecticut, Enfield Public Schools)

Because the universe is a whole of laws nothing is done according to random manner. Any construction in the universe is done under laws of the concrete space. Space is a whole precisely determined. In such case any construction is formed with the inheritance characteristic of the whole. Particularly visible, in the case of a basic matter state change where a square is also a centered form.

	5 - From the tangent point and the center of the square draw a segment intersecting the two opposite edges of the square. This problem is resolved because this segment is the diameter of the circle solution. Its location is at the square center.

6 - The transformation of a square into a circle is done in the conservation of surface. This circle of a square is the reciprocal of the problem of squaring a circle.

- EVOLUTION OF A CIRCLE (USA)

Before there was only a Central Symmetry space. Then actually, the universe is built on along the evolution of a circle from where space structures unveil for unbounded constructions.

- squaring the circle (student.harward.edu, USA)

- Vietnam buddhist circle and square (sbcglobal.net, USA)

- intersecting circle plan (Canada, Ontario, Ottawa Carleton University)

- distinguish a circle from a square (China)

Circle is The unique form in the universe.
From circle, one can construct any another form. While any another form can't never be transformed into a circle whithout using the unique ultimate way of transforming circle into square.
This is the proof of the fundamental unique event of the universe beginning.

Conclusion

The surface transformations are in both directions between a circle and a square. These operations are reversible.

Proof of the universe Evolution

- The + Earth + is + square. + what + facts + prove + this + statement + wrong (Guyana)

The first obviousness proves that the Earth is round as a sphere. Thus, the Earth form as a square is wrong.
But language is a bad means of science when we are confused language as law realities. Generaly, everyone can use a same text of language to interpret and to states his own law differently to the other ones. Thus, when the Anciants stated that "the Sky is Round, the Earth is a Square", it is quite an error to interpret this expression as mechanic form descriptions.
The Earth is a square is too much difficult to understand its meaning. In fact, NOBODY understand it as the Beginning of physical law transformations of the universe construction. This is only the consequence of the Mathematics' impossibility in constructing the Squaring a Circle.
Logically, when the basic human reasons is nothing else than a unique Circle concept nobody can't never know what is a line. Next, he can never know what is measurements of a length. Therefore, we can tell that without another form than the circular one, there is no possibility for a human to tell that "I know something around me, because I can't know and measure what is a Distance".
It is why, according to that beings are on the Earth, we can tell that the Earth is alive because we know what is "Here and Over-there, Here and Now".
Therefore, as the sky appears only with Round movement of stars while we can see that Life on the Earth is at least the possibility to now what is a Distance. As any Distance is refered to the the cardinal points one can tel that the Earth is a Square as Life symbol.

Finally, telling that the Earth is square, is logically justified when one can have somme understanding about the law generation in the universe.

In such case, the universe may enter in a close loop operation and indefinitely squaring a circle then next circling a square, in a perpetual motion. In this case, the Whole is a set of elemental matter always turning around and do not know any construction. But this is not the reality. The proof of the Evolution is according to the consequences of the necessity to change in square form that allows movements to build. As soon as the universe had squares a circle, there was only two logic choices :

The proof of the Evolution can be stated as follows :

1 - As a Whole, anything necessarily happens in the Whole universe. 2 - The matter is in the Permanence of a perfect central symmetry of non-interacting movement in a pure elemental gas. For the purpose of construction, the matter must initiate a change in this structure of movement. This first unique action concerned necessarily to change from a perfect central symmetry into a nearest form that is a square. Therefore, on the result a such operation leads directly to the following form where the universe was going into. 3 - The first change of form is a canonical one and has the property of to be reversible. Consequently, there is Two solutions for the results of this First universe action. a) - Either, the matter change is in random manner, in this case the universe should oscillate perpetually on both the reversible changes between a square and a circle, that is starting building and starting demolition. Thus, in random manner, no consistent construction can be done even during a short time. The average is that no change appears in the Whole universe and nothing is yet existing. The probability of construction is as the one when the universe is playing heads or tails with a coin. There is fifty-fifty for constructions and demolition! b) - Or, the squaring a circle is actually a logic potential of changes for Successive Constructions, then, the universe is really starting its first step on a way of unbounded Life development. Therefore, the result of the First action of the matter is now obvious : a) - Either there is nothing to know b) - Or today, Life is necessarily existing. If we are here discussing on our beginning, it is clear that there was no alternative. No alternative because there was not a random manner in the matter logic. We have introduced the random action because the First action is reversible. If ever there existed a random factor, then necessarily the reversibility should lead on the choice of a close loops one. Therefore, considering the reversibility of the First action, we can conclude that there is both no random action and only the unique usefulness of this First action is a logic rational departure. The universe is today existing, is really the proof of a precise departure of the universe going in Evolution. And this evolution process follows an unbounded way of uniqueness, as we can proven it in the matter structure. The uniqueness means that Evolution means forward changes and never in a close loop. Signification of the reciprocal of a matter transformations A transformation is done according to the matter logic which is the Permanence of Construction. Construction acts in Succession. Phenomena happens only according to these logic. This means that any phenomenon is a step of a construction successive process. Thus a phenomenon is included alwayss between a Preceding and a Successive one. This is not the description like a motion differentiation but is fundamentally successions of an interaction flowing in other different interactions. Along this path of succession, there is generally a means to find the logic of the reciprocal process which seems that a natural phenomenon may return to its initial state and thus produces null changes in the nature. In consequences, it may happens that Changes in the nature may return back following its path of the preceding state. And according to this, it is possible to the universe to return to its birthday. From this conclusion, one hopes the possibility to make journeys through the Time successions. About this there are great discussions on the reversibility or the irreversibilty of the physics processes. However, these are only beliefs and confusions between phenomena that is matter construction and the logic of its processes. Matter is the Permanence. The Permanence is not an abstraction, a hypothesis or an ideology. The permanence is the basic of the logic thought that processes also, in successive manner because thoughts are also matter logic constructions. The reciprocal of a phenomena is not a backward transformation that is a contradiction to the Succession logic. Therefore, a reciprocal transformation should be considered as a new transformation that use a same logic. Only the forms seem to illustrated a return operation, e.g., as a cyclic rotation. In a rotation, although it seems to be a forward and backward motion, but rotation is also and is only, a Succession of motion. We know its with the Earth, alwayss in a cyclic days and nights, nevertheless, no tomorrow is never like a yesterday. And the belief that transformations are falling in a deterministic direction, is of the same class as the cyclic hypothesis. Succession in nature are a specific processes that build Uniqueness and do not run in the sameness and monotony of an positive growing Entropy belief. Thus, in the nature, there is only Successive transformations for new constructions. The reciprocal of a transformation is a quite different transformations where the different states of matter are quite different. Because the Succession involves that any transformation is standing between its preceding and its successive ones. And the logic are : each succession has a unique preceding. In brief, there is no cyclic or deterministic transformations in the nature. According to these logic, any object should wear in it the information of its preceding state and also the potential of its successive state. The reciprocal of transformation concerns only a logic notion that have the following meaning : Changes follow a different ways but necessarily and sufficiently, are done according to the same Permanent logic of matter and only with it. In consequences, there is no Causes in the universe. Because matter transformations depends on the condition of Preceding of any object. Therefore, if there is a Cause of this transformation, this Cause should depend of the object Preceding information. This is a contradiction, because a Cause do not depend on its effect. The same analysis may be applied to the Random processes. The definition of this latter is that it generates an unpredictable event. Now, if an object transformation event is dependent to the object Preceding states, we can say that any matter transformations is necessarily foreseeable. In consequence, in the nature logic there is not Random transformations. This is why one can tell that the universe is perfectly rational. These matter logic properties give birth to the knowledge of the natural number series and one can say justly that this natural numbers are the universe archetype. The successive constructions in the nature give to this numbers series the characteristic of the recurrent struture of matter. Quantum Matter is an indestructible and immutable quantum of matter. From this objects construction are done in succession of condensation of this immutable elemnt of matter. It is why we have the Recurrence notion. And the Recurrence is a physics concept that means "sucessive add of a unit". Any unit, can be used as a kilometer, a yard, an inch, a bottle, a astronomic unit, a sandwich, a drink, and so on... The condition is that this unit should remain constant, along the transformation series. It is why there is a most important fundamental notion to established. We must remind that ZERO IS NOT A NUMBER. And the natural numbers series must begin only with a unit One. If there is a Zero number, the matter does not exist and there is no universe because this latter is built with the Recurrent Process, that start with a concrete One that is a concrete quantity added for constructions. Zero is only a very useful writing symbol, as the "space" in a text and as the "rest" in music. In summery The reciprocal of a matter transformation, is only a different particular logic in matter and is not a reversible or a cyclic transformation. The rotation of a wheel is not a cyclic motion because each state of a rotation is different to the another owing to the Recurrent or Successive process that performs an ADD NEWER for transformations. It is the same for the Entropy deterministic process, that is an unjustified and bad observation of the nature, ignoring the natural Recurrent construction process. In the nature there is only Evolution of matter constructions. And the Succession is a Logic Function of matter that may be analyzed with the canonical circle and square transformation logic. The Successive Function is a real perfect Recursive Function of Life according to that newer Life can be formed and so, objects in the uniqueness can exist in nature. This is the marvel of the matter logic, simple but generating unbounded wealth for Life during Evolution. For Life, the Recursive function of Life may be tell as follows : any Life can get a Change-of-Change-of-Change-,etc... That is Life can be developed in a wealthy unlimited manners. The Recurrent Successive is a perfect recursive process, and is not an abstract mathematical notion. It is a physical one, the most basic, and give to us the two permanent notion of : the Just and the Goodness. The Just, because any particular life in the universe can access to this Life Function. Goodness, because Life can be developed as vast as any paricular life needs it. We must not neglect the human feelings that are not irrational phenomena. In the contrary, feelings come from our deep links with the matter physics. This are done in a so vast reading of nature information in our Self and generally can not described with standard words of a language. But the feeling of everybody should be considered as having roots in natural phenomena. - zero + has + no + reciprocal + proof (India) And also,there is no logic for a direct proof of zero. Zero is a most useful invention. Because it is a language symbol and not a quantity. And zero is the consciousness of the starting point of a length. Thus, a segment is only a segment if it is defined by both the two extreme sides, for example A and B. With AB we can get a real length while only with B the is no knowledge on the length of this segment. The length unit denoted as ONE, remains an unknow length quantity in the successive number series. But when we can take conscience of a starting point A, then ONE becomes a concret unit quantity. For example, with thousand apples how can we count them as a qunatity of thousand fruits? We only get the knowledge of thousand apples, If and Only If, a symbol zero is introduced in these apples. In human language, we denote with the ZERO term. But in these apples, it suffice to mark one on them the signification of that, is the starting and also the ending of a count. Thus, with this marked apple, we can now always tell that there is 100 apples after counting them starting from the marked apple and ending the count when we reach this same marked fruit. But really, this marked appel is only the Starting point and not the Ending one. Because when we tell: O, 1, 2, 3, 4, 5, 6, 7, 8, 9, The successve integer of this series, is the 10. And the 10 with a zero, means that it is the Starting for an another decimal base count. Even if we start from 20 and go bacward with successive precedent numbers, when we arrive to the 10 and after that to the zero after the ONE, this zero is not the end of the series. IT is really only the CONCEPT OF STARTING POINT. The fact that there is the convention of rational numbers, the négative number id not a backward count, but a forward negative number. Thus any series of quantities begins fron a starting point conventionally denoted as a zero. The Zero is not a number, but it is the concept of a Starting or origin of a quantity to grow or to decrease. The division by a zero, not-a-number, is only an artifact of arithmetic and algebraic conventional methods where exists the infinity realm.

Analysis of these Dakhiometry methods of changing surface forms, one can however find that although the operation are reversible, the way of changing a circle into a square is more straight forward because it is more simple and the change of a circle needs not a square form to succeed the transformation. While when changing the square into e circle surface, the square needs to know the circle form. This means that the squaring a circle is anterior and remains in memory before the circling of a square can be done. Then, the squaring of a circle is really the first changing action in the matter. And matter did not hesitate indefinitely to start at a glance, the universe Life Evolution, to square a circle, when it happens !

Proof of the First action
To square a circle, is an authentic First Transformation of the universe for this reasons :

1 - In the state of matter where no interaction had yet happened, the universe with its movements was in the state of a perfect central or axial symmetry. In this situation, the only logic was only of "circle" form. This means that any movement in the space is only in rotation mode. One can say that the Thought knows only the rotation.

2 - To begin any construction, matter must change its initial movement state. Thus, it must square a circle because the most nearest form of a circle is the square. In this action, matter use necessarily the only logic of circle forms. This is why squaring a circle can be done necessarily and sufficiently with "circle tools". We can say also, that the square is the first step or the first knowledge of logic of Life's thought. Therefore, it is a true when the Ancients said that "the Earth is Square".

3 - In the case of the inverse operation, that is to circle a square, the use of circle tools is allows, because we can say that the thought has evolved and in the universe memory, there is now, at least, the knowledge of the circle and the square. Physically, on can say that movement for the beginning of complex construction, is now in the Liberty of choosing a local-omnidirection where translation and rotation are combinations for building a complex object.

4 - these analysis and remarks areas not extreme because these matter transformations are not only problems for mathematics specialists. Remind that the Dakhiometry is really physics knowledge of the matter. The consequences of these basics operations of the nature are unlimited. In the next texts, it will be show rationally why one says that transformations yin and Yang, with that, anything is a composition of yin plus Yang. Here the yin and the Yang may be represented by the square and the circle. In a more general expression, it will be proven the logic of the real and necessarily Complementary of Components in the construction of Life. The square and the circle are really the mutual complementary. And one can find the necessarily mixture of the yin and the Yang in matter. And the universe construction uses this necessarily basic logic to go in the Endless Recurrence. Note that The yin and Yang are not the duality of "contraries". The world Complementary is more just and more precise the process of the "memory generating new thoughts that add for newer memory". This the basic of the notion of the natural universe Direct Democracy.

- Knowledge + of + the + Dao + Duc + of + the + universe (comcast.net, California, USA)

Dao-Duc-Kinh disignates the The Virtue Way book of the Anciant Lao-Tseu. Virtue means there the Just and Optimal action. Then it is the book of what about the whole universe a human science is concerned. The Ying Yang logo is welknown as originated from there. But it may also from the anciant Buddhism and more largely from most of anciant human legend from anywhere on the Earth.
Its No-action Wu-Wei is in fact not the passiveness for human. But it means really that universal laws have not to act or to decide to resolve any problem. According to the Dao-Duc-Kinh, universal laws are not a Will. They are only the BEING. Therefore, the No-Action means there that if man is one with universal laws, one have no need to act. The Dao-Duc-King's No-Action means that the No-Action is only the perfect universal knowledge, the aim of the Virtue Way.
In modern time we can tell that a human true science should rests on the best knowledge of the universal laws.


- Tao + Te + King + summary

For the Dakhiometry, this First action in the Primordial universe state, is only a change in movements. From the perfect central symmetry, a change of movement direction is done according to the Liberty of movement direction. Rationally, we say that movement are free in the homogeneous and isotropic space according to the Motion Conservation of the Whole. Thus, the first change of motion is not a mysterious "Effect following a Cause" because the Conservation is a permanent principle of the permanent matter. Therefore, the First action of the universe is not a creation. The Permanence of matter is a fundamental necessarily logic, the same that our thoughts is constructed and that allows the Uniqueness.

- dao + duc + kinh (Australia)

- DAO + DUC + KINH + TE (Vietnam)

In the Tao-te-king (also say as the Dao-Duc-kinh), the book of the Wisdom, Lao-tse had mostly described the Breath or the matter elemental gas dakhi. The language form is only a one that suited the way of understanding particular to a mode of life in a Earth region. However, on the whole Earth, the Ancients knowledge seems to be a same universal and rational knowledge, that only is not so obvious because of the different language forms. Any Ancients knowledge in any country, is really rational and universal. Only because of a misunderstanding, human a separated by theirs believes that give the supremacy of a form on an another one. In no doubt, there is really a Babel Tower.

One knows the Anaxagoras' model of the universe as a cloud of elemental matter. His problem was how from this elemental particle matter, everything can be formed and the validity of a movement as a whirlpool can begin. This model may be influenced the Descartes theory of the nature that abhors the void.

In fact, the gaseous elemental matter and the non-void of the matter are the reality of matter. Because Breath of universe matter is a very dense quantum matter. It is as dense as the dakhion and the locations of space ares separated each from its neigbor by an elemental length, the Planck's length. Why can it be a so dense matter while human can experiments the spatial void? The gaseous dakhi is dense however is invisible and inperceptible to any object because of its two fundamental properties. The first is its fineness and the second, its immutability and indestructible particle state. We do not go through a wall because its matter is coarse and the unsteady of the chemical molecules. This means that an interaction with the wall, is done with friction where energy is dissipated. While the dense indestructible dakhi do not interact with any coarse matter and interactions in this gaseous elemental matter are done in frictionless manner. This is why the dakhi is also a dense memory of the universe.

And finally, the dakhion needs not a hypothetical whirlpool where no conservation of movement is conceivable. The dakhi is a permanent structure of space and movement and matter has the property to appear only in central symmetry. Therefore, the staring of the universe construction is only a logic of the movement behavior that stays in the primary central symmetry structure of matter, as a potential of starting constructions. This potential is in fact the property of matter to behave in construction as a recurrence process from that anything has the capacity to be reproductive.

The significance of the universe's First Action

The Fist action in the universe is thus well defined. Starting from the Permanent Being of the matter space, a change in the movement structure had its reason in its potential of change. This action is not due to a random process and we can say that the creation notion in the same class of events.

Creation and random process can happen anywhere and at anytime and are Causes that do not depend to the Effects. We have demonstrated that the first change of form is done according to the Principe of the Surface Conservation that is the Matter Conservation. Surfaces are quantities of the indestructible elemental matters in a form of a plan. These surface transformations are reversible. Therefore the reversibility and the conservation of matter are preexisting conditions and means that the First Action in the universe are not Creation and the reversibility is contradictory with the random events, because the reversibility is rational property. It is why demonstration of mathematics theorems are done generally in the direct and reciprocal ways as a reversible rational knowledge. The hazard is contradictory with the reversibility, because the reversibility means a rational knowledge that is anterior to the event. Therefore, when you know a event that will happens, there is obviously no random event !

The First change of form in the universe is then rational beginning of action that obeys to a matter logic. This means that what happens next to this change has a rational development.

We can understand why the Ancients had passion of seeking the method of squaring a circle. They had a real intuition of the importance of something very deep behind this understanding. In fact, the transformation of forms to reveal a square is as a gate opening on the universe existence, the starting of Life construction. Because the square and the circle are the logic of the Complementary of Life. The two parts complementary cans thus give the meaning of the Successive constructions that unfolds in the Recurrence along a way.

In summary
The beginning of the universe is a unique logic in the matter. There was not a little chance for random processes in this beginning of Life. Just next to the First change of form, according to the properties of the Succession and the Complementary principle, it should be revealed the model of the Life construction in the ubiquity of the ONE of a Whole. That is to say that the model of the universe construction must appear at once, as universal model of matter construction. Thus, after the squaring a circle, The two Complementary forms are a logic that fills the entire universe, because a logic is validated in a whole universe plan and the matter dakhi is a physical property of transferring interactions in frictionless manner in the ubiquity mode of the memory. The rational knowledge of Life is revealed in the matter "at a glance" as a universal property of Life should be. No hesitation is allows, because anywhere in the universe, Life can begin to construct in a same logic of matter.

Therefore, at this beginning of the First Change, any first constructions should have the Knowledge of its Being and with the reveal of the universe model, each have the Knowledge of Counting. I am ...you are ... he is ... and One, two, three, and its successor is four.... Since this beginning, Life is growing in the multiplicity.