Rational Cube Transformations
by Nguyên Tân Tài
How to Transform A CUBE VOLUME.
The consequences of its resolution.
 angle + trisection + best + results + 2011 (Egypt)
a) In the meantime, the meaning of doublingacube resolution is also an equivalent importance for year 2011 events on Earth.
b)  Squaring the Circle, Trisection of an Angle and Doubling a Cube are three hugue rational and basic Portails for accessing the universe Space.
c)  Stating them as Impossibilities is as prohibing the freedom for human thinking.
The DoublingaCube is not a simple gadget, a Ticks of Mathematics. Telling Doubling a Cube seems to be simple. But as like an ocean, one can't achieve its end because this ocean is no more than the universe space. Its worth more than any weight in gold. It ruins the Irrationality.
 transformation + of + cubes (India)
What are Mathematics Impossibilities
Impossibilities of Mathematics are originated from the Mathematic Numbers system. It drives to the Mathematics millenary impossibility to resolve three main basic problems in science:
a)  Mathematics Transcendental Numbers.
b)  Mathematics Irrational Numbers.
1)  There is no Transcendantal Numbers according to the Squaring a Circle resolution where the Number Pi is rationaly constructed and is not an undetermined Transcendental one.
2)  Irrational Numbers as the (2^{1/3}) is a false statement that rests on a false argument statement as due to the irrational (2^{1/3}). It is proved in this texte with the complete resolution of the Doubling a Cube conjecture where the (2^{1/3} can be precisely figured out as a length.
Consequences
a)  One of it immediately consequence is that the Third Root of any Quantity can be defined accurately when the Dakhiometry spatial language construction is used.
b)  It shows the fact that universal Laws are expressed only in a plane or only in Two Dimensions Space.
DOUBLING THE VOLUME OF A CUBE.
 impossibility + of + doubling + cube (..)
 double + the + cube + of + length + z (mycingular.net)
This the exact general definition of this doublingcube problem.
It is according to the spatial construction property. One have only to construct the structure, whatever any initial unit defined for constructing this figure.
 doubling cubic (Serbia)
 doubling + cube + proof (Serbia?)
 how does the volume of a cube change if its dimensions are doubled (Mexico)
This problem is a direct one that can be resolved by a current linear calculation.
The following inverse problem is a more difficult when it concern to find The Exact Given Part that composed precisely an initial Given Length.
The problem is from a given volume of a cube how to double its initial volume.
This is a well known millenary problem about which Mathematics states as impossible to geometricaly resolve because the Third Root of Number 2 is an irrational one. It is underlined there that irrational Numbers is mathematicaly defined as being not a finite solution from a division.
However, this is a bad, false and conventional definition. It is due to that Mathematics knows how to do Number division only with the euclidean division algorithm. But this latter is by itself an "irrational" imprecise method for exact division. Most of Number division are then an open loop operation that never be ended. This unprecise method is badly extended to Geometry so that the irrationality definition was extended as "irrationality is unconstructible number of the Geometry". From there necessary, one understand that the universe space is composed of Space HOLES. The universe Space is then mixed with Nothingness for the current Mathematics! The conclusion is a doubt about the oddness as: "Why a Nothingness can be mixed with the concretness of a space volume?"
For such DOUBT the Dakhiometry can give a precise proof that the irrationality is no more than mathematicians' fantasy. It concerns to the rational answer that the Third Root of Number 2 can be rationaly constructed.
The LENGTH of the Third Root can be figured out by spatial construction using the Dakhiometry Spatial Language Method:
The DOUBLING OF A CUBE CAN BE RATIONALLY AND EXACTLY CONSTRUCTED.
This present text exposes how the Impossible Doubling a Cube can be rationaly and simply resolved.
The Doubt is about:
1)  Do the Doubling a Cube be an Impossible construction?
To prepare some answers it should be necessary to get the factors that may characterize the uniqueness for a more precise conscience concerning this problem.
All what mathematicians conscience that has until now done on the doubling a cube, was the ThreeDimensions of a cube. It is from such main factor that any mathematicians falled to have a more precise possibility for some solution. It is not with different types of parabola and hyperbola that they can found some key for a precise answer. Thus, with:
DoublingaCube = 2.(Cubeside)^{3}
or
Solution of final CubeSide = (cubeside).((2^{1/3}))
Mathematicians will get and another doubt following the doublingacube one. This is the new doubt about:
Is ((2^{1/3})) a constructible Numbers?
We know that Mathematics response is to state the Impossibility of this problem resolution.
The Dakhiometry preparing to concretly and precisely structure its Doubt
 hoe does doubling cube work (pavlovmedia.com)
 doubling cube Vietnam (Germany)
 examples of doubling volume in math (k12.or.us, Oregon)
 transformation + of + rectangular + form (banglalionwimax.com)
There is relationships between parallelepipede form with the cube one.
 if + the + length + of + each + side + of + a + cube + was + doubled + what + is + the + corresponding + effect + on + the + volume + of + the + cube.
Initially, if side is X, then cube volume is X^{3}
Now, this cubeside will be 2.X
The final resuling cube volume will be:
(2.X)^{3}
But not as a double cubes like,
2.(X^{3})
 prove that if a "mumber" is double than its cube is 8 times the cube of given number (India)
[(2x)^{3} = 8. x^{3}] ???
Or also interesting:
[(y.x)^{3} = y^{3}. x^{3}] ???
This seems to be an odd thing isn't ?
However, the Dakhiometry is also a top oddthing.
Here next is shown what was developed this interesting Dalhiometry method, a one for kids, never known to overcome this last strange formula to allow the whealthy rational and magic pratical tool for any volume transformations.
 If + the + sides + lengths + of + a + cube + are + doubled how + does + that + affect + the + volume + of + a + cube (east.verizon.net)
These next figures show the result of final Cube by doublingSide of initial cube. The result is then:
[(2x)^{3} = 8. x^{3}]
The basic general reason is proved in the following...
 The Dakhiometry magic Transformation tool is as follows 
Application From
 single + cube + transe + formation (..)
 single + cube + transformation (..)
 single + cube + transformation (optonline.net)
Here is a general process to transform a givencube form in any cubic volume needed...
Therefore,
A world where any being should be necessary defined in a cubic form then,
any of their tranformation is possible !!!
In fact, this can be stated more generally as:
A world where any being should be necessary defined in a same GIVEN COMPLEX (or not) FORM then,
any of their tranformation is possible !!!
If a such world is with the complexity independent from Form then, this world is valid with the Unity principle. This means that a such world is also in a wealthy complexity one !
It is the case of OUR UNIVERSE!
Coplexity in our Our Universe is independent from any FormorAppearance !!!
Fantastic isn't !
A basic real fantastic Unity principle.
 singie + cube + transe + for + mation (India)
Resolutions from the Dakhiometry language is easy and rational.
Note that with the Spatial language there is no problem of figure scale. So for precise tranceformation of an atomic cubic form or the one of a heavenly body one have only to go in trance by choosing the unit scale of one's figure.
 single + cube + transe + for + mation (VietNam)
 algebraic proof doubling the side length of a cube multiplies the volume by 8 (cox.net, Kansas)
The proof is there seen under the algebraic form.
However it is here for a best understanding by the current mathematiciens that are formed only by Algebra.
This problem was not yet proved by the current Mathematics even under algebraic method. This shows that the algebraic tool by itself don't allows to do such proof.
Therefore,
According to the 3D view of a cube the question is:
Where is there any questioning about doubling the side (L) of a cube?
Isn't the answer so practically obvious?
Thus, if there was probkems about doubling the side of a cube then, this situation is due ONLY to the difficulty induced by the usual algebraic formation in Mathematics. Simply, Modern Mathematic is strctly thinking the world through the Conventional Numeric as the Archetype of the universe!
But the origin of the proof gives here can be successfully done only with the spatial method. In fact it is ONLY the spatial construction that enlights the understanding of such problem.
So on this next figures it is only the included figures that explain this problem.
The given algebraic formula are only as a for best understanding to mathematiciens with their usual algebraic capability.
Contrary to the Algebra where a (1) is only a conventional Unit. But what is a number (1)? Does it represents anything.
What means: 1 duck = 1 dog ?
But one should note that:
Only the unitLength of a figure is the basic reason for starting any spatial construction.
The unit is the concrete Reality for all of this given figure transformations !
Therefore, only the spatial concept can give some clear understanding on such problem when one knows that a spatial figure begins at first by defining a trueglobalconstantUnitLength.
The basic Unit is not the anxiety for the Algebra.
While for the Dakhiometry Spatial Language, a spatial figure should represent the True Universe Space Reality. Because with the Dakhiometry Spatial Language, one should maintain a Constant unit of the figure according to that any transformation by addition, substraction, multiplication and division should be coherent to all the figure... according to a Constant defined UnitLength of the figure!!!
It should be at least a such discipline for sciences when considering real phenomena... You may note that it is not the dead Geometry worry.
Also one may note that it is the highly concern for any C.A.D. software used in Technology where a figure should be a true exact ratio of the reality!!!
Thus, it is forward when the questionning is being uniquely and globally resolved by spatial construction:
"prove that if a number is double than its cube is 8 times the cube of given number"
Therefore,
The algebraic form given next is strictly an information formalism but not a rational method. It is indicated here for mathematiciansofNumbers in the form of Numberformathematicians.
But the Numbers is so poor method:
Can Numbers give any answer for adding, substracting, multiplying and dividing any solid form ???
The Dakhiometry can resolve all these problems...
by using the authentic rational Universal Spatial Language.
Note that the Spatial Language is not the anciant's Geometry. This latter is simply a language using drawingfigures replacing Words for talking discourses.
While the Dakhiometry Spatial Language is the direct equivalence of the alphabet elements of the universe matter.
A rational construction with the Spatial Language is simply the direct image happened in the real universe space construction by itself.
If one need an example:
The Spatial Language construction for the Squaring the Circle is the direct equivalence with the Real Space property. Only such rational science allow the True Exactness of the Fundamental Space Constant.
It is note also the case for resolving not only the Trisection of an Angle but the capability of the Addition, Substraction, Multiplication and Division done directly on any given angle in spacialform (not by using the anciant's Trigonometric Number). This is directly the construction of AngleTransformations.
With the Dakhiometry Spatial Language Science get there, the TopBasicKnowledge for understanding the whole universe construction in Space.
Actually,
the universe Space is not the Anciant's Nothingness...
Well, owing to the Nothingness at least, the Rrelativity theory is Something.
However, whithout such real knowledge with the Spatial Language concerning the universe Absolute Space as scientific capability there is no possible man's science on the universe matter else than by amount of socalled scientific hypothetic presuppositions.
As for an example: the science darkness on basic problem of how to define the masscenter of any object. It is note that necessary, without a given masscenter, there is Nothing...
No surprise that proud of such ignorance drives to the fantastic Relativist SpatioTemporal Thing !
 single + cube + transformation (seznam.cz)
 cheetah + roaring
Out of politenes yes. Cheetah head off as strong as a Lion Roaring.
If + you + double + the + sides + of + a + cube (cisco.com, s. Colorado)
 if + you + double + the + length + of + a + cube. + What + do + you + get + (mathematics) (South Africa)
Note on the Dakhiometry Recurrence principle
The Recurrence of the Dakhiometry is only the valid one.
Because a recurrence fact should be come from more basic reason of the Absolute Space foundation and the definition of Elemental of the Discrete Matter.
The old Recurrence from Descartes is only a notion from man counting "One bird, two brids, three birds,..." and on modern Integer Numbers Theory. A such Recurrence is only an evidence from everyday practices. Recurence founded on the natural Number is a contradiction when a successive Number meets a Zero! This is because a Zero is an impossibility of succession !!! Also if integer numbers beging from a Zero than there is no possible succession. That is to tell in the Nothingness there is never a successive property as possible Recurence fact. Thus, the succession from Zero also it is a fatal contradiction!
One can note that between Obviousness and Principle there is usually only confused worlds of languages.
Therefore, the Dakhiometry founded on the proved Absolute Space where are necessary defined location situated between one another preceeding and follows by a succeceding another one. This is the true rational definition of the recurrence. Because a Recurrence should be necessary a repetition of an elemental same matter fact property.
If "One bird, two brids, three birds,..." seems ti be a recurrence then:
"One bird, two brids, three birds,... four cow, five cow,..." then, it is not a recurrence because birds and cows is not as same facts. Even if the same talking language of number can be applyed to count them.
Only the Dakhiometry Absolute Space can constitute the Source of the Recurrence principle.
 bdouble + cube (Russian Federation)
 most difficult thing in modernmathematic is (amazonaws.com, uswest)
One with his back to the wall when concerning to traduce what are from algebraic into Spatial figure constructions. This is due to the irrationality of conventional number system as interpretinglanguage.
This latter can't be adjust to the reality of the Space.
Algebraic language is a dream that clash on the reality.
 if a number is double than its cube is 8 times the cube of given number (United Arab Emirates)
 does doubling the volume of a cube have the same effect on the side length (milwwi.sbcglobal.net)
Effectively, the difference is as follows:
1)  Doubling the cube volume (V) is a linear volume function:
[ 1(V_{x}) + 1(V_{x}) = 2(V_{x}) ]
2)  While doubling the side (x) of cube is done as a cubeprogression of volume:
[ (V_{x})^{3} ] ...>>> [ (V_{2x})^{3} ]
Here following are concerned the Doubling of Cubevolumes.
 how + can + you + change + the + edge + length + of + a + cube + so + that + its + volume + is + doubled (rr.com, California)
 how + can + you + change + the + edge + length + of + a + cube + so + that + its + volume + is + doubled (cspirefiber.net)
There is two manners to resolve this problem:
1)  Or adding two same cubes then, it is what was resolved in this present text.
2)  Or using this presently resolved problem to start as reciprocally method. This is to start with this resolved problem as:
[third (root of 2)] multiplyed by the side of a given cube.
This is to tell that this present resolved problem according to spatial construction,
can be applyed in direct and recirpocal manner to double a given cube volume.
 doubling + volume + using + cubes (Australia)
Actually, it is a fundamental case.
Because as for the aera case where the basic square is necessary, most of volume determinations rest on the cube one as their transformation root !!!
For example, by precise construction, one can double the volume of a sphere, an elipsoide, an ovoide, a paraboloide,... and consequently, any defined complex linear form, inscribed in them.
1)  What is Doubling a Cube?
This is simply what is shown on this next figure.
Associate 2 volumes of a same cubes to get one bigger cube
However, the problem is that the direct association of 2 cubes don't produce directly a cube form but a rectangular polygonal form as is seen on this figure.
Therefore, the problem of doubling a cube is the difficult one as follows:
How to transform a rectangular paralellepiped into a cube of the same volume?.
 doubling + and + tripling + dimensions + of + a + cube (sbcglobal.net, Texas)
The proceed is to gat from two given cubes, to construct a common cube face for thess given cubes.
To get a common aera of a cube face, it can be construct the realtionship as follows:
Let two cubes with sides as,
(x.x.x) and (y.y.y)
It can be transformed as:
(x.x.x) as (x.x.k)
With:
(x.x.k) = (y.y.y)
Or,
k = (y.y.y) / (x.x)
Therefore, (k) is then known to perform addition between thes two parts.
The main problem in space is How to TransForms.
 problem of doubling the cube (VietNam)
 volume + of + matter (cox.net, Philadelphia, USA)
 doubling + volume + of + a + cube (bc.edu, USA)
 transform + cube (Thailand)
 prove + doubling + cube + impossible (verizon.net, Washington DC)
We have seen How to transform a Circle into a Square form.
The Squaring a Circle, the Doubling a Cube should be more precisely tell as:
How to change the different forms in the universe 3dimensions space without changing any of their another basic characteristics.
The impossibility of Mathematics constructions is not due to the Irrationality of the Space. It is due ONLY to the Mathematics false concepts on the universe Quantity, expressed with an artificial system of Numbers created from the man's Talking language. Thus, naturally words of Language, can never be constructed with the space elements as tools of construction to represent the universe Quantities.
This Numbers system of Mathematics will obviously produce the Impossibility due to the Nothingness. Nothingness is the Nothing. Then it can't never represent any of the universe realities. The BlackHole are from the Nothing type. Then it is a heavy contradiction for scientists who believe that a Nothing belongs to the universe reality.
Now,
Why the Impossibility of the Doubling a Cube can be easily resolved with the Dakhiometry Method?
There is a grand reason in Dakhiometry that allows to get a just knowledge on the universe of physic realities. This is a basic universe Fact, stated as follows:
Postulate on universal laws:
The Universal Laws expressed their activities ONLY in TWODIMENSIONS.
It is this true basic postulate that we will proceed to the Doubling a Cube resolution as exposed in the following.
Dakhiometry method to transform
a rectangular polygonal form into a cube one of same volume.
Applying this preceeding postulate, we can determine the just good factors that allows the transformation process.
Thus while tempting as the Anciants did it without any success for resolving this problem, it concerns to choose what factors may represent justly the Doubling a Cube operation.
All these choosen factors should be representative of the problem in a common one plane where are acting the corresponding universal Laws.
Examining the above figure it can be seen that after associating the two cubes, there are two planes sufficiently representatives of the transformation operation.
Thus, in the rectangular polygonal form, there are 2 faces on which one can proceed the corresponding transformation of form.
It is the face sides of the polygonal form that are:
a)  ABCD
b)  BCEF
This two faces will be put in a same plane to form a common specific structure of a Doubling Cube operation. This structure allows to use another basic form representative of the doubling operation. Because THERE IS NO POSSIBILITY to use directly the INITIAL FORMS to solve this problem!
Here after, are the universal laws instructions for use:
In the chosen structure on a common plane:
1)  Represent the aera of ABCD by the square of SIDE equal to their AERA quantities.
2)  It allows to get two representative squares ABCD and BCEF.
These two aera ABCD and BCEF are representative of the initial total volume.
3)  Therefore, the transfomation solution into a square of the 3dimensions polygonal form is done when:
The Cube solution is get when the final cube TWO FACES SQUARES ARE IDENTICAL BETWEEN THEM, according to that the 6 faces of a same Cube are identical.
 what is a cube (UK)
Problem Entrance for it resolution
 volumetric + monuments (Iran)
 square + cube + calculator + South + Africa (South Africa)
 make + a + concrete + mathematics (rogers.com, Canada)
Pourquoi une démonstration par construction est UNIVERSELLE?
 le + cube + impossible (acndigital.net)
Note pratique importante.
Il est réalisé la construction de volume double d'un cube de (2unités de côté).
Cependant, il n'est pas nécessaire de le faire à chaque fois, pour toute autre dimension de cube.
Pourquoi donc?
Vous avez ici, la présence de la richesse du Langage Spatial qui n'est que le langage d'expression fidèlement direct de la Réalité de l'espace dans lequel nous vivons.
Le Langage Spatial est un langage SgnifiéEtSignifiant, celui directement de la Réalité du Monde. Le langage de l'Espace est donc directement la Réalité qui Signifie ses Réalités du Monde.
Alors que pour l'homme, le langage parlé n'est qu'un MOYEN CONVENTIONNEL pour Signifier SEULEMENT.
La différence est que le langage parlé de l'homme ne raconte la Réalité que selon la capacité de l'homme de connaîtrecequel'onestcapabledeconnaître. En bref, le langage parlé de l'homme n'est que ce que l'IGNORANCE DE l'HOMME lui autorise de "dire".
Ainsi, le Langage Spatial est directement la REALITE BRUTE du MONDE. Et la Réalité brute de l'univers est UNIVERSELLE.
Voici en quoi, nous allons illustrer cette Vérité
1)  Le doublement d'un Cube est ici réalisé par construction Spatiale sur un cube de départ de (2 unités) de côté.
Si cette construction est rationnelle, alors nous pouvons conclure que sa solution est nécessairement UNIVERSELLE pour Toute dimension de cube.
2)  Pourquoi donc cela estelle une vérité?
Car, avec les Nombres algébrique et Arithmétiques, chacun est persuadé que les nombres [(2): (3,7 ); (0,71); (113,03);...), sont tous différents les uns des autres. Et même que chacun a une signification particulière dans sa vie.
Or, la vérité est comme ceci.
Une construction spatial peut se faire à partir de n'importe quelle unité car, une Longuer n'est qu'une Longueur... relativement à la structure dans laquelle elle appartient.
UNE STRUCTURE DE L'ESPACE EST UNIVERSELLE!
C'est la différence entre la Dakhiométrie et les Mathématiques courantes qui s'encroûte dans la Nombres, Archétype du MONDE.
Chacun peut construire une MêmeFigure dans la dimension qui lui convient, pour retrouver la Vérité universelle d'un théorème. Ce qui veut dire que: SEULE ET SEULEMENT, la Certitude est Universelle. La Certitude ne dépend pas des conventions des Mots utilisés pour en parler.
En conséquence
La démonstration du problème de Doubler un Cube, lorsqu'elle est Vraie sur un Modèle d'unitédelongueurdonnée, est NECESSAIREMENT VRAI POUR TOUTE autre échelle de DIMENSION car, UNE STRUCTURE DE L'ESPACE EST DANS LA PERMANENCE, VRAIE.
Pour quelle Raison peuton se reposer?
C'est que, l'unité dans le langage Spatial est indifférente pour la vérité d'une figure de construction donnée, parce que:
La PROPRIETE DE L'ESPACE EST D'ETRE PLEINEMENT HOMOTHETIQUE, par cette même raison, qu'une Structure, fussetelle homothétique, est dans la Simplicité, VRAIE.
Si donc chacun des Nombres est un Ego à part, il n'y a pas d'universalité par les Nombres. Ceci est directement l'effet du Conventionnel du Langage Parlé ou Ecrit, dont le sens Signifiant souffre de l'inconsistence de l'ignorance de l'homme par laquelle ce langage est institué par chaque ego qui parle.
En conclusion
La démonstration du problème de Doubler le Volume d'un Cube, s'il est vrai pour le dimension d'une longeur de 2unité, est donc NECESSAIREMENT VRAIE POUR TOUTE AUTRE DIMENSION.
Pratiquement, il suffit de faire l'homothétie de cette construction donné dans ce texte pour n'importe quelle UNITE DE FIGURE PAR HOMOTHETIE.
Si l'on veut dire simplement avec les techniques d'imagerie modernes, il suffit de projetter la constrution de la démonstration, par projection sur un écran de dimensions voulues, pour Doubler un cube de la dimension de l'Ecran de projection.
Voilà ce qu'il faut comprendre, pour ne pas rater la nouveauté que je présente ici. Autrement, les esprits demeurent dans l'éternité des vielles casseroles millénaires de Mathématiques, enfermés dans le caveau par les Dogmes.
Si cela vous intéresse d'avoir une conscience plus précise sur la Langage Spatiale, examinez la Quadrature du Cercle de la Dakhiométrie donnée en ce Siteci et vous verrez ce qu'est le langage d'étude de l'espace Dakhi selon ses Structures. La Quadrature du Cercle y est donnée pour une dimension de quatreunités de côté du Carré. Cependant que cette Vérité est strictement Universelle.
Defining the problem Entrance
For a regular polygonal solid, its volume may be represented by two of its faces.
a)  In the case of a cube it is two of its adjacent faces.
b)  For two adjacentcube with face against face, it is here represented by the two faces as:
(ABCD) and (BCEF)
ABCD is a face of Rectangle type. It is easy to transform it into a Square with the LamCa theorem.
Thus for the final Cube solution we have to work its volume on the base of this two initial unequal faces (ABCD) and (BCEF) as shwon on this next figure.
Transforming polygonal form into Cube one.
This is the Dakhiometry principle of the DoublingaCube basic resolution.
However, a such resolution is still impossible for Mathematics capacity. It is because Mathematics ignores the Spatial LAnguage.
It is because Mathematics Ignore that there is an Absolute Space where everything is exactly defined by structures. It will be exposed in the following how to place this two choosen square aeras ABCD and BCEF in a solid basic space structure.
Note
The socalled Pi for this DoublingaCube, is the Dakhiometry one.
If you use your old Archimedes' Pi, this problem can never be resolve and the (2^{1/3}) found will be not the exact value!
Dakhiometry method for transformation
How changing or equaling two squares of different dimensions
For a constant rectangular or cube volume.
THE DOUBLINGACUBE WAS EASILY RESOLVED WHOLY OWING TO THE DAKHIOMETRY LAMCA THEOREM
All the steps of constituing the DoublingaCube resolution can be donne by calculation directly in the DAkhiometry spatial language. But for more shorter and simple explainations, il will be donne in a mixed Number expression and in spatial language construction.
Let an initial given cube of (2x2x2) volume Its one face is denoted as BCEF.
Doubling this cube is to associate succesiveley two of this cube.
It gives two different one parallelepipede faces as:
ABCD and BCEF
with successiveley the aeras:
ABCD = 8
BCEF = 4
Associate 2 volumes in a same cubes to get one bigger cube
These two rectangular square and rectangle, will be included in a structure of two square with a common summit (O), as shown in this next figure.
K2 = 8x8 for (ABCD) aera
K1 = 4x4 for (BCEF) aera
 how + to + get + the + volume + of + a + cube (sbcglobal.net, Texas)
 4x4 + cube + word + meaning (Cambodia)
This two squares represent a structure corresponding to the aeras of BCEF and ABCD rectangular polygons.
Initially, this two aeras values are different. The Doubling a Cube consists to change the forms of BCEF and ABCD in such manner that they will be both 2 squares of same aeras.
This transformation is done on the representative structure of two squares K1 an K2. The sides of (K1) and (K2) have respectively the aera values of BCEF and ABCD aeras.
The principle of this construction is that:
The different aeras of BCEF and ABCD will be equal when they takes both the same ARITHMETIC AVERAGE value from their initial aera difference. Then this two aeras are equal and take the value of:
Solution of Doubling a Cube = (8+4)/2 = 6
for each of them.
But this construction is not directly done on these two different aeras themselves.
It needs only to work on this structure (K1+K2). Their sides represent directly the interested aeras. This operation is done precisely. Note that or the squares or the circle (K1) and (K2) can be considered for this transformation.
Construction for transformation of two Cubes
in One with their total volume.
Preliminaries
The Doubling a Cube is a main occurence to show that without knowing the CircletoSquare transformation, one cannot resolve the SquaretoSquare one.
It is the Space Constant that can prove precisely the Doubling a Cube. The old mathematicians belief currently denoted as the Aechimedes' Pi is ONLY a coarse approximative Trick to serve as craft recipe for representing a circle.
But to precisely measure the Cube transformation, the Space knowledge is needed. Because this Doubling a Cube should be constructed wholy with the spatial language.
 cube abcdef (Hungary)
It is this form that allows to transform any other volume form into a cube and inversely.
I will expose next this basic transformation method in whole spatial consruction done from the beginning to the end of these constructions. This allows to compare the difference between the Numeral calculations with the precise spatial construction proceeding with lengthes.
It appears that any square root done with the current calculators using Numbers are not the exact values.
 convertir la surface rectangulaire en circulaire (Morocco)
En effet, c'est par la structure cerclecarré que l'on peut réaliser cette construction.
Transdormation for equality of these two aeras BCEF and ABCD.
It is used here the Circle (K1) and (K2) to define the equality of their aeras. In the meantime, this Space Constant is denoted simply with the currently use as the "Pi".
The Spatial Constant is given by this numeral formula:
The space constant has nothing to do with the "Pimeter" who was an empirical notion of the Anciants. At their Time they was woried by the difficulty of practical measurements on a circle.
Differently,
1)  The Space Constant is directly and wholy, the basic vast concept of the universe Absolute Space.
2)  It is also the case for tha LamCa theorem, which is not a simplistic summation of to squared conventional Numbers. The LamCa theorem is a pass for travelling throughtout the universe Space for transforming aeras and volumes of matter.
Note that the DoublingaCube resolution is no more than simply, the direct result of the LamCa theorem application.
 réalise une figure polygonale, les patrons d'un cube (Portugal)
 doubling the cube definition (Latvia)
 doubling + the + cube (Hong Kong)
 when + the + volume + of + the + cube + is + doubled + how + can + I + find + the + length (ctm.net)
 math + doubling + the + cube (Mauritius)
 doubling + cube + impossibility + proof (Poland)
 double the "gievn" cube (optonline.net)
Construction for Doubling a Cube
Steps of construction
One know how to calculate a circle aera (S) with the diameter (D):
S = (Pi/4).D^{2}
The structure drawn in blue are squares and circles with the side and diameter equal to the aeras of the two choosen (ABCD) and (BCED) faces of the above initial quadrilateral ABCDEF.
1)  Thus the first step consists to calculate the aera (1) as indicate on this figure. It is equal to the arithmetic average from the circles (K1) and (K2) aeras.
The circle (1) is determined as follows:
a)  Determining aera circle (1):
The different aeras are:
K1 = (4^{2}.Pi/4)
K2 = (8^{2}.Pi/4)
Then:
aera (1) = K1+(K2K1)/2.
Next, the spatial construction is successively used:
2)  The diameter of (1) can give its square root using the unit length position. This square root is the diameter of the circle (2).
3)  The square root of Circle (2) diameter define the diameter of the circle (3).
4)  Then the square root of the circle (3) diameter, figure out
the length (OM) equal to the THIRD ROOT OF NUMBER 2.
The final results are:
1)  Circle (1) diameter is:
Diameter of circle (1) = ((2^{1/3}))^{8}
2)  Circle (2) diameter is:
Diameter circle (2) = ((2^{1/3}))^{4}
3)  Circle (3) diameter is:
Diameter circle (3) = ((2^{1/3}))^{2}
4)  Finaly, the square root of Circle (3) diameter is:
Square Root of diameter (3) = ((2^{1/3}))
The Doubling Cube solution is given by the circle (2) diameter.
Diameter circle (2) = 2 . ((2^{1/3}))
It is the SIDE LENGTH of the final Cube with the double volume of the initial given cube.
Initial Cube Volume = 2.2.2 = 8
Final double cube volume = [Diameter circle (2)]^{3} = 16
Different construction steps for Doubling a Cube
This animated gif resumes the different steps
to construct the DoublingaCube.
 doubling + the + cube + example + and ++ proof (Philipinnes)
This following next figure illustrate the step of how to get the average of two aeras and from there how to get finally the thirdrootof2.
This allows to perform the Doublingacube by the formula:
2.(n^{3}) = ThirdRoot of 3).n
Where (n) is the initial given CubeSide for doubling this given Cube.
This resolution is fully done by space construction.
This doublingCube is resolved on the basis that a Cube is a volume that all its aera Sides are mutually equal between them.
There are some decimal discrepancy between the results getting from the current existing numeric algorithm of calculator. But the Spatial constructions are necessary exact by itself if the figures are done precisely with a good (C.A.O.) software.
 how + can + you + change + the + edge + length + of + a + cube + so + that + its + volume + is + doubled (comcast.net, Georgia)
If only there was one given cube then doubling this given cube consists to resolve this problem as the reciprocal manner of the above solution.
This can be done for any initial given cube.
The Mathematics Impossibilities are only from the darkness of Mathematics Believes.
It is urgent in Sciences to replace the Pi=31416...,
And then,
 in any application and also for any theory 
immediatly replace it with the following rational SpaceConstant.
Without such correction,
nothing in any rational science won't do at all!
The present DoubligCube resolution shows the serious systematic errors introduced by the current false Pivalue 31416...
Introduction
This present DoublingaCube is mainly at first: to show how to determine the ThirdRootof3.
Because if we suppose that the algebraic ThirdRootof3 is given as:
Current ThirdRoot3 = 1,2599210498948731647672106072782...
obviously for every body,...
length of Numbers means BigPrecision.
more Number = High precision!
Then calculation of any cube volume by [AdditionSubstractionMultiplicatioDivision] can be done in the SpatialLanguage as follows:
Let:
(Vx) the desire Cube Volume to find.
ThirdRoot3 = R_{3}
and finally, any cube volume is given by this simple formula:
Vx = (R_{3} Side)^{3}
These calculations can be done precisely relatively to an initial given CubeSide by Spatial Construction.
However, the difficult problem of DoublingaCube is to determine the
ThirdRootof3
... which is the current Mathematicimpossibility.
It is why this present Text shows how effectively to resolve the determination of:
The basic ThirdRootOf3
However,
The problem is that this text shows that there is a discrepancy between:
the ThirdRoot3 by Construction
Compared with the ThirdRootof3 given by the current Algebraic numericdéterminations.
These differences between the Spatial Construction and the one given by the classic NumberCalculation,
is here to pointout that the dicrepancy between the Spatial Construction and the algebraic determination is due to:
The Archimedes' Pi (3.1416...)
Because any C.A.D Software numeric calculation rest on the base of the Archimedes' Pi.
The discrepancy of results is due to this bad foundation of numeric calculation system
where systematic error is about as high as 1.01.% for any figure of circle used in figure constructions.
Adding to this,
a)  Errors of figure drawings.
b)  Errors introdced by the Euclidean Divison.
c)  Errors due to the artificial the socalled precise Real Number system.
And now, the error of eveybody interpetation, that sytemtically uses to compare the results of the new Spatial Language method with:
HIS Eternal Perfect and Artificial Algebraic Number calculations!
Now, transforming Forms as Squaring the Circles, transforming the Cube Volumes and Transforming the Space Direction  the so called Trisection  can be rationally done PRECISELY in most simpliest manner for the Dakhiometry Spatial Construction.
The basic knowledge to get is the Squaring a Circle transformation. Without such performence nothing can be exactly resolved.
It is because the Basic property of the universe space is the Circle. Thus, any construction is derived necessary from the Circle.
Without knowing the exact circle measurement, every construction remain imprecise. Because a Circle is not defined by the Mathematics classic 3.1416... This latter is the root of systematic error for any current construction process.
The fortune is smilling to human because the Squaring a Circle needs only to know the RATIO between the Circle and the Square.
The Dakhiometry Constant is the PermanentTrue CircleValue.
It is why we can't get effectively this Exact Ratio for any duo Circle/Square obtained as:
This Basic exact SPACE CONSTANT is purely a RATIO!
The ratio between any Square Side and its correponding circle Diameter... as the Dakhiometry proved it.
The problem is quite different when concerning to determine the exact Length in the case of Doubling the Cube!!!
And excactly, one needs there to use the True Circle Perimeter as function of its Diameter Length!
Why a such severe condition?
Simply,
it is because the Universe Constructions are founded on the Circle Structure!
We have to be in conscience that there is no Hazard with the Universal Laws.
Every existence in the universe is born from the Circle properties.
Note on updating any Numeric Processor
Probably in the meantime,
For the current C.A.D. software, if suffice for uddating the Pi value to add an subroutine to introduce to any Numeric Processor the choice for the New Pi Value getting from the Squaring the Circle.
It is important not only for Precise Sciences but also for Technology where the Circle is also the Basic mechanic forms for modern Mechanical Sciences.
Doubling a Cube ???
No nead to scratch one's Head !
I tell that:
The SquaringaCircle was the Biginning of the Universe Construction !!!
How can one begin to construct any thing, if one had not any tool and any proceed to build something ???
It is why as soon as the SquaringtheCircle was done then every construction was ON THE WAY.
This means that the SquaringaCircle is by is not only the Beginning but it was the Fact of any construction in the universe is currently ON THE WAY !
What are then the real basic Facts of the SquaringaCircle?
I)  The universe in its Circular Permanence before its construction is a Whole Circular universe of NoForm Matter, it was the matter state of the Dakhion. According to the Principle of Energy/Matter Conservation the whole space of the universe is by itself ONE ELEMENT Dakhion, in its elementalmatter state and according to its ubiquity property, anyoneDakhion is both occuping its elemental form and also the Whole universe Space. It is the rationalPermanent reality Fact but is not an illusion. Before the Beginning the universe is Both a Huge and also a One elementalMatter. This means that the universe Matter was in no Form Matter before the Beginning of its construction. There was no change in the universe. The Permanent Conservation Principal was fulfilled.
II)  Thus, the matter transmuttation giving the SquaringaCircle fact is by itself a First change in the Matter. This initial Change in the Space is directly the event of the universe Launching in Construction.
III)  If there was beginning og Construction, then there are necessary the Tools for construction. More, if there was Tools for construction then, there are necessary Projects for Construction. However, this statement is only an anthropomorphic idea. This latter is a real fact for Man because Man is second order of construction from Matter. For the universe Beginning it is only an initial First Step of Matter Starting in Construction. Therefore, The universe Matter beginning in construction by SquarringaCircle, is by itself creating BOTH the ToolAndTheProceedsOfConstruction. More easy to understand, the Beginning by SquaringaCircle should be understood as wholy:
The beginning of the Universe Construction by the SquaringaCircle is simply the universe Definition of the Set of the Universal Laws.
IV)  Now what are at least the Basic Laws for MatterConstruction???
Remind that Before any construction in the universe, the Dakhions are the Matter State of NOFORM. The universe before and after construction is then in the same Permanent volume. According to the Matter Conservation principe the universe Space is necessary with Permanent Absolute space Volume.
Therefore,
What are the Basic necessities for Matter CONSTRUCTION? They are necessary concerning the Volume in the universe Absolute Space. The Basic Universal LAws for Constructions is then Concerning the Universe Space Proprties:
It consists of Law for defining in the universe Space:
1)  The Laws possibilities for defining Distances and Directions.
2)  The Laws possibilities for defining Matter Aeras.
3)  The Laws possibilities for defining Matter Volume.
We can see that there are too much thing to do in the universe for starting the Beginning of Constructions... Particularly, according to our antropomorphism we may believe that it need too much Time and Delay for succesfully preparing the Beginning of universe. Thus, is Mattter an enough good Thinker? What can does the SquaringaCircle for such so complex Jobs ???
However, its needs no Philisophic, no Physical capacities and NoTime needed for the univers Matter!
Mays be, Universe Matter is rather really SuperMagic. How can it be?
The responses is simply:
With ONE operation as The SquaringaCircle, the universe of NoFormMatter, is doing a multiplecomplexoperations as Creating Tools and Designs for Launching the Constructions in the Univers.
The ONEUNIQUEOPERATION FOR THE UNIVERSE GOING IN CONSTRUCTION IS THRE SQUARINGTHECIRCLE.
This is shows as:
A)  The Most Basic Forms as [Circle and Square] was created by One SquaringtheCircle.
B)  The Universal Spacial Laws for the Tool of Constructions are created in the same SquaringaCircle operation.
a)  From there the Space Alphabets for constructions are defined as LOCATION, DISTANCE and DIRECTION.
b)  It consists the defition of ratio Proportions between the CIRCLE/SQUARE AERAS and VOLUMES... and consequently, the AERAS and VOLUMES OF ANY OTHER FORMS.
c)  From there, any Matter Construction rest on this CircleSquare Template for FOUNDING the Universe unbounded Complex Constructions.
Conclusion
Why did I expressing the Basic meaning of the Squaring a Circle as the Foundation of the whole universe Physic?
It is because of the so called Squaring a Circle, the Doubling a Cube and the Trisection of an Angle. These socalled fantastic Mathematics Impossibilities. This is real true characteristics of the Man's Primary Mathematics.
The present DOUBLING a SQUARE, is really impossible. This a Fact. Because even with the Dakhiometry well defined SpatialLanguage, I can't resolve the cumbersome (ThirdRoot Of Two) according to the Algebraic Resolution of the ThirdRoot of Number.
I give here in this present text the reason as:
The modernalgebraic ThirdRoot of (2) is not and can't be the exact resolution. This is because the algebraic give an ABSOLUTE LENGTH for the Root3. The imediate contradiction is that the Mathematics rests simply on the universe as simple Nothingness. The Contradiction of the Calculation by Numbers proceed is given the ThirdRoot as an ABSOLUTE SOLUTION: the so called:
ThirdRoot of 2 = 1,2599210498948731647672106072782...
As excat or unexact solution,
a Such absolutevalue is contradictory to the Mathematics Nothingness universe. Therefore this numeric calculation is necessary no valid because it repudiate the belief of the Nothingness.
It is why the Dakhiometry spatiallanguage can catchatshadow of the Mathematics.
But the Dakhiometry know to calculate all the Aeras/Volumes of any Forms according to the results of the Squaring a Circle consequences.
It is because the SpatialLanguage can calculate any of Distance and Aeras and Volumes and also the Angles of any Form in the universe.
This is to tell;
The solution of NumberRoots should be given directly from the SquaringtheCircle template !!!!
It can be given any Length, Aera and Volume of any Form when the Squaring a Circle was initiated the Squaring a Circle in the Universe for any Construction !!!
For example it can be transform the volume and the aera of a sphere by using the Squaring a Circle model!
This shows that Mathematicians are close up for a long time in the Mathematics Bilieves.
The Suaring a Circle that is revealed by the Dakhiometry is simply for most of the current Mathematicians no more than a simple intertainement fact... Mathematicians are not in conscience of the SquaringtaCircle large range Solutions.
Doubling a Cube ???
This Job is wholy done by the Dakhiometry.
According to the exactness of the Dakhiometry Spatial Language
it need a specific high precison C.A.D. with well inside Dakhiometry SpatialConstant inaccurately currently used with the Old approximative Pi.
Here next are given whole process of the Dakhiometry Transformation of any given Cube Volume.
Here how to construct the Basic Constant Factor of Cube Volume Transformations.
This figure shows precisely how to construct the Basic Factor for general VOLUMETRANSFORMATION.
From the known ThirdRoot2 Length this following next figure shows example with Cube Volume Transformations.
It is noted that Knowing Cube Volume Transformation the Spatial Language allows to TRANSFORME VOLUME OF ANY FORM !!!
 image + and + definition + of + duplication + of + the + cubes (Philippines)
It is difficult to get the understanding of thes figures for doubling the Cube.
This because the Dakhiometry Spatial Language, is not known in Mathematics.
The Spatial Language is mainly considered that any figure construction, is DIRECTLY the representation of the SPACE elements.
As when one is constructing a building, the Figure of an architec is directly the Spece Representation by Point, Lines and Curves. These representation is then the direct precise measures of the building.
It is also for the Spatial Language where figures ARE DIRECTLY, THE REAL SPACE REPRESENTATION.
This is quite different when one is using the Old Geometry. As for the Number Sytem, Numbers and Geometric figure are simply conventional shematic but not the true equivalent to the Real Space. Geometry and Numbers are Conventional symbols as for example (a, b, c,...) are for the talking and writing languages
Figure of the Dakhiometry can be considered as Direct Constrution with the Space Alphabets. More, the Dakhiometry Spatial Language, need not as in Geometry, use the Numeric calculations for determining the different measures.
With spatial Language, a figure is directly formed with the real measures of the Formes structure.
There the Add, Sub, Multiplication and Division are done directly by figure constructions by calculation. The present doublingacube is example. It is why it is difficult to get the understanding of figures. Theses doublingaCubes figures are direct calculation meaning of (Cube.2) or (Cube/2) as Cubemultiplications and Division and not by geometric trial/errors results!
It is why there is difficulties for understanding the combinaitions in the Dakhiometry Figures without having the good acquaintance with the Spatial Language Direct CAlculations of represented figures.
For the different presents figure on DoublingtheCube, there are difficulties for everybody to get immediatly the understanding of these constructions.
It is also for me, there are myself difficulties to represnt Figures that may be understood by Mathematicians. The Spatial Languages is FAR FROM THE ANCIANTS' GEOMETRY!
It is why there are Too much Impossibilities foe Mathematics to Resolve many numeous Problems added to there the Mystic Irrationallity of their Numbers and more rigidities of Nothingness presuppositions as Infinities...
The Dakhiometry had also resolved the AngleTrisection for any angle in the whole 360°. But there are too much works to represent its to the Mathematicians the mind rooted to the spot by Millenary Mathematics continuing education!
In Fact and really, ingnoring the Spatial Language, is for ever beyond Rational Sciences. This is not to overestimate the current Science problem.
The above figures are concerning the Cube Volume Transformations.
There are some error in range about 5%. This is vithin the error due to the current Mathematics Archimedes' Pi value.
The length calculation mode of the Spatial Language is not to be involved. Spatial Language Length calculation is quite precise. Points definition are well resolved and precisely defined. There is no irrational Holes. Line of Points for calculation are optimally defined by the Numeric Processor of current C.A.D. softwares.
The only error to be implicated is the Error from the old classic Pi of Mathematics. It is about 5%.
One can see that the Spatial Language method for Lengthcalculation is quite using wholy the Circle. It is the proceed that mathematics of Number algorithmes are quite ignoring.
It is why it is urgent to change quickly any numeric device to be replaced with the New Pi of the Dakhiometry particularly for the enhencement of the whole industrial world where at first technology is concerned. More basically, scientifc precise calculations are also the most important of interest where an error of somepercent is really a terrific disater.
Here next are concerning the Constructions for Miltiplication and the Division of SQUAREAERAS.
Next is the same but Reciprocal Constructions.
These figures show how Spatial Constructions as true Language are easily explicit for understanding and mastering phenomena of Constructions in the universe Space.
These figures are explicite by itselves.
No need to produce long discourses.
In summary
To overcome the MathematicsComplications is not to cover in glory!
The numericcalculation of RootOfNumber is for ever only Mathematics artificial Tricks of the TRADE. The Number as Archetype Trade of the so called Universe Nothingness!
No more doubt that it is not from rational sciences.
How mastering the Volume ThreeDimensions is for the Spatial Language a more too simple real rational science of the universe SpaceinConstruction!
Transformation of Volume is too difficult for Mathematics because... because it is the most simple and precise process Fact for the Dakhiometry.
No need there to catch at shadow and to run after the Infinity!
It is only necessary to beging to get acquaintance with the True Language of the universe Space.
The Dakhiometry is not a ghost attached at a Mathematics Branch where Mathematics is the Tree of all man's Knowledge, even if it is the belief for any mathematician!
The Dakhiometry is purely the Universe RationalPhysicsScience.
One should see that the Dakhiometry is strictly manipulating DIRECTLY THE MATTER. This latter is simply POINTS, SUCCSSION OF POINTS in Circular manner. What is the universe Physic? The universe Construction is strictly formed with such matter ultimate states. Therefore, the Dakhiometry is using directly this basic matterstate to get the knowledge on any of the Universe Transformation for Construction!
It is so simple to tell it. However, it is simply but directly to be an integral part of the universe matter and particularly also to be in integral part of ourselve, our physics and our knowledge.
One needs only some exercices to get quickly in acquaintance with the true accurate Spatial Language, THE ULTIMATE LANGUAGE directly use by the universe Space for Construction
and also,
it's the Human's ULTIMATE SCIENTIFIC LANGUAGE!
I am not a Mathematics vassal. So if one is continuiting to integrate the Dakhiometry into the Mathematics System then I will stop to talk about the Dakhiometry possibilties.
It may be the fact.
Because I am too aged and too tired to be abble to have sufficient Time to reveal the large possibilities of the Dakhiometry knowledge concerning the rational Realities of our Universe.
 what + is + the + name + of + the + object + formed + when + doubling + a + cube (South Africa)
May be, any of the different BasicForms. Because from a given Cube may defined any of the Basic form, for example: a sphere, a polyedre, a cylinder, a pyramid,...
Here in this present text, only square figure are representing the corresponding cubeface. Figure in Threedimensions are only for representing mirages of forms. Its all an act.
The permanent unhealthy science ignorance belief
What is the source of the current science ignorance?
Answer:
What is the Linearity?
Liearity is the man acting as a robot always going straight toward a target.
The Big current ignorance is to stay in the belief that one remains strictly in his primary unhealthy belief that his knowledge thinking world is quite Linear. Then from such capacity man is going directly along a pefect Line to get any reality in his surrounding World.
This statement is only for describing the main current knowhow state.
1)  The Dedekind presupposed KnownCut about tempting to catch in Liearnly manner an unknown Thing. A "method" with what every Sciences are fully in agreement:
2)  The Archimedes's running after the UnknownCircle with his known polygon. On such result dictatorially rest modern sciences.
What is the Linear approaches to reach a target???
Basically, Linear approach is only to define a Straight Line between Two Points A and B.
With such job, necessarily these two Points should be known to form a Straight Line.
Is it the famous Euclid's Line?
Not AT ALL!
This Euclide definition is a rational true definition. Even it is a false definition of a Straight Line. Consequently, the Dynamics First Newton's Law is also NOTADEFINITION of a Straight Line Motion. It is not sufficient to use the word StraightLine to be a scientific statement! Why ???
Simply, a Straight Line should be defined PointTOPoint. The Euclide StraightLine definition is the definition of ONLY TWOSUCCESSIVEPoints and not any A whole straight Line!
For the Newton's First Law, it is then unsufficient to tel that Uniform motion is a Straight Line!
Also, the Einstein Continuum is is then the antidefinition of a Straight Line. It is because in an UNDEFINED Continum there is no Direction to define the notion of the Being Straight!!!
With such example, on can see that the current Science Theories rest on the NOTHINGNESS! Without such elementary concept Sciences rest steadily on True Solid Nothing. This latter is simply the Total Ignorance of true and real Science Objects.
Thus, with modern technology, one can believe that Precision means for example:
3,141592653589793238462643383279....
It is quite the illusion of Linearity. The endless decimal can never be significant as going to the extremum of the Precicion. It is only to catch the shadow. The Prey is not there the Point (B) of a line (AB). It is because there is not any Straight Line (AtoB). It is only the euclidean Belief. The Einstein's Relativities is a true according to that it is a trueignorance.
So all these are to means that there is only the Impossibility to Know or the Impossibility of Man's Knowledge ?
Not any. we have not to find comfort in the Impossibilities.
There are only huge man's Ignorances.
Linear belives come from man's ignorance where nothing is weell defined. According to the Dakhiometry, there is no STRAIGHT LINE as defined by the current Sciences according to that Line is Two Points. Such definition is issue science opinions.
Line is never a twopointsthing!
Line of the Dakhiometry DiscreteMatter is a Continue Successions of elemental MatterPoints. Therefore, a real STARIGHTLINE SHOULD BE DEFINED AS POINTTOPOINT SUCCESSIVELY DEFINED.
This is contrary to the usual millenary Euclidean Definition of current sciences.
And Now what is in fact this Dakhiometry StarightLine?
The Dakhiometry STRAIGHTLINE is Simply a DIRECTION of the universe Space.
And,
A Line (AB) is simply a LineDISTANCE.
Consequences:
A)  Precise science is concerning the distance. It is concerning TWOPOINT (AB) Distance where (A) and (B) should be known to be abble to measure their Distance.
B)  The necessary condition of measuring a Distance (AB) is foundamentally TO KNOWITSDIRECTION.
C)  Therfore, MEASURING a Distance (AB) need to know Basically Two Factors:
1)  The two end (A) and (B) of the search Distance.
2)  And to know the Direction of (A and B) or (B and A).
These are the foundation of reality Knowledge.
In summary,
Precise definitions for measurement need to define at least:
a)  To know the Locations of two Points.
b)  To know the Direction on whith these two Points are found.
Here next a current practice for precision definition of two Points (AB) in archery sport. The archer is point A and the target center is point (B):
The problem is there to define the arrow impacts.
Is there some possibility to apply the DedekindCut even if one knows the target Center?
Thus, it is not the distance of the impacts that allows to define precisely the target center.
However, to define preciely this center, the main factor is not to know the lateral Approach of impact.
The true problem is basically for the archer to know the Direction of the Target Center. The direction where the arrow follows to heat the center that depends to many other unknown factors.
Therefore, the Dedekind and the Archimedes' approaches are not the most efficient method to get the Precision even if sciences are currently recommand it practice!
Clearly tell,
the lateral Dadekind's and Archimedes' approaches is quite false because their precison point is not defined by a Direction Factor:
1)  Lateral approach is from man's incorrect Linear conventional method.
B)  While A Direction Factor is from the universal Space Circular property.
Correct precision in science should be based on the well defined properties of Circle... at least on the Space Constant... badly defined with as the conservative name Pi.
Even if Man is rather conservative but sciences should rest on the most precise ways.
Even if conservative is man's problem however, concerning the Dakhiometry Ideal precision of Space Constant this latter defined at least still Twenty years is not not yet as general use in sciences!!!
It is still a gadget in the Fantastic Museum of Curiosity!
Is there really some human's Modern Science on Earth?
Now an another curiosity on precison.
Do one knows why the Precise Suqaring the Circle is yet possible?
The Basic response is:
The Squaring the Circle is possible according to that this Problem was resolved by the Dakhiometry method for it Resolution based on the Definition of the SpaceDirection!
You are invited to revisit the SquaringaCircle Proof and you will see that the Proof is really based on how to Determine the Key as the Direction in Space for the Universe Beginning!
It is the Direction that allows the Precise SquaringaCircle Fact and then, the Beginning universe SpaceConstant!
 area + of + a + circle + A + pie + r + where + PI + (pie) is + appoximately + equivalent + to + 3.1416 (Philippines)
The circle area seems to be a light approximation of about 0.006% when using the 3.1416. However, it is because only this application is a particular case of a pratical current use.
But the true general use of the Pi as a Space Constant in figure construction need a more precise true value.
It is the case for the Dakhiometry Spatial Langauge where Numbers are not used but only precise spatial Constructions.
The Pi is generaly used in modern Astronomy and Cosmology. Particularly in the Statistic Mechanics and Particle Sciences where the different probability models need the constant of Pi is frequently use. There in the scale of particles for example, with the different Constant as the Planck one, it needs a 10^{35} precision. In such applications, it can be seen that the circle area error of 0.006% is really a hugue error introduced at any step of such long calculations.
Here next represents the spatial comparison between the Archimedes' 3.1415... Pi and the squaring circle one.
It consists from a given circle perimeter 16 to calculate this circle radius R to note the difference of these values. It is used the formula:
R = 16/Pi
A numerical calculator is used with its Archimedes' Pi and also with the Sqaring Circle Pi. Even if the Calculator has its own Algebraic method errors, however these errors are the same and is canceled in this comparison.
With the calculated radius, it is now using the compass to drawn such circles in concentric points with their radius differences. This figure shows a great difference between their spatial constructions. The more greater the given perimeter is, the more is the difference done as:
n*P = n*R
A such so great error is unacceptable for the precise spatial language. As the squaring a circle produce a rational and absolute precise length of Pi. The usual Archimedes' Pi is unvalidated for modern sciences and most current mathematical calculations produce really unexpedted and confused values for modern precise sciences.
It is noted that the same calculations done by spatial language on these formula, produce point to point concordance for the same value Pi of the squaring circle. While it is also different with any other tiny difference with this Space Constant length!
More when science will be in use of the spatial language and it will be necessary in the futur to be in acquaintance with this such true basic method. In the use of space, a point is a perfectly precise point in construction. There is no approximation possible as one used to be in compagnonship with the Archimedes' Pi in the Algebraic mode. This latter introduce another unknown approximations due to the false concept of quantity when one use the Numbers and all its irrational method as the Real Number Line. In a such world where everything is approximative there will be no more science than the usual consensus of scientific "guilde dogma", as it is the case with the modern sciences.
There are some values dicrepancies concerning the given ThirdRoot
between the Dakhiometry constructions
compared with the usual numeric calculation done with a digital calculator
The question is:
1)  Is the Dakhiometry construction an incorrect process?
It is easy to verify it.
Let us beging the DoublingCube construction using a starting value for the circle (1) with its diameter as given by the numeric calculator as:
Diameter of circle (1) = 6.34980420787279789
2)  So using the same construction starting from this circle (1) to get finally the circle (4) that give the (ThirdRoot of 2).
3)  It will be seen that these construction give excatly the same value of (ThirdRootof2) as given by the numeric calculator.
We can see that the Spatial Construction is an exact process.
There is no default in the Spatial Language construction.
However, the problem is that if we beging the construction by starting from the same structure given by this next above figure, the final value for the circle (1) diameter is not equal to the one given by the numeric calculator!
As the Spatial construction is a precise one the reciprocal operation should be a true one.
This shows that the Numeric Calculation is incorrect according to that the reciprocal calculation of ThreeRoot is not True.
The Spatial Construction is quite reproducible and correct.
Therefore, the numeric calculation for ThirdRoot is NOTEXACT !
This shows that it can be verify any exactness by Spatialconstruction with the Numeric Calculation given by any usual Calculator.
Concerning this next above figure for determining the DoublingaCube, the differentce between the averaging operation that allows to determine the Circle(1). It is correct as an arithmetic averaging between Length2 and Length8. This give averagingLine denoted as (Average) on the figure.
But there is a difference between this Averaging value obtained by construction and the numeric one that is as folows:
The spatial construction gives the average value as:
2 + 3 = 5
While the numeric value that give all of these ThirdRoot numeric calculation is getting by calculator as follows:
(1,25992104989487...).2 = 2,5198420997897463...
(2,51984209978974...).2 = 5,0396841995794926...
And this value (5,0396841995794926...) is different with the averaging value 5
Thus, the circle (1) diameter equal to:
5,0396841995794926...
is exactly the value for the reciprocal construction that allows to construct the circle (1) and
to get finally the numeric ThirdRootof3 as,
Thirdrootof3 = 1,2599210498948731...
Conclusion,
A)  The Spatial construction is a regular exact process for calculing any length as well as by direct calculation and its reciprocal one.
Note construction by figures furnishes always the reciprocal solution.
B)  But for the usual algebraic numeric calculation, the thirdroot of Number is not given a regular result all along the same calculation for all the number series.
Thus, it is not sufficient to judge the exactness of Spatial Calculation method by considereing these results with the so called numeric calculations algorithms using the algebraic Numbers.
In the contrary,
defaults of numeric calculations should be clearly seen when proceeding with the well precise Spatial Calculation Language.
The spatial language is simply the property of real physical SpaceElements as Locationpoints, Distances and Directions used for any transformation of forms during constructions.
All transformation operations are well defined in Spatial Construction for example the basic ones as Addition, Substraction, Multiplication and Division.
There are yet to much things to get for being in acquaitance with and to master the requisite basic Spatial Language. However, it should be the fundamental tool for getting a correct understanding on the universe Physics.
NOTE
All these above calculations can be performed entirely and precisely with the Dakhiometry spatial language.
This means that the (2^{1/3}) is completely constructed and precisely figured out. The Doubling a Cube is also generalized as the Cubic Multiplication and Division.
What does it means?
Simply that any universe Quantity (x) can be (x^{1/3}) by constructions, without finding Irrational Nothingness.
Generalization of CubicTransformation
Cubictransformation is denoted for transformations Cubes into Cubes.
The Doubling a Cube is only a particular case.
Generalization of cubictransformations can be extended as Cubic Multiplication and Division.
It is noted that:
Any operation on Volume Manipulations (Addition, Substraction, Multiplication and Division) is wholy performed with the DAkhiometry Spatial Language!
It is according to that from Circles/Squares forms as aeras or Volumes, it can be derived any other basic Forms.
The doubling a Cube shown here is ONLY a simple elemental transformation.
Really, Mathematics and basic sciences are simply from PRIMITIVE proud man with his Amont of Tricks and recipes the man firmly still staying in his unintelligibility.
Modern Marhematics is still as the earliest form of man in the Universe Space blindness.
This is the fact of a sad reality!
The Impossibility Theorem is really the concret current Man portrait.
 cube + volume (Vietnam)
 cube + construction + and + volumetric + divisions (India)
Actually.
When mltiplication (or addition) can be constructed then the division is the reciprocal one.
 transforming + cube (ua.edu, Alabama, USA)
Note on the Doubling a Cube method:
This present adding of two equal Cubes to make one with a double of volume is only a particular case of figure. But any of forms can be added to get finally one cube with the resulting total volume.
It need to proceed no differently than as indicated in this text for adding two equal cube.
With the Dakhiometry spatial language for construction, it is easy to resolve any addition of two or many different volumes in any forms.
For example, we have to add two Cube in two different volumes:
a)  We need first then to define one face of these cubes being in equal aeras.
b)  This imply that one of theses two cubes will be a parallelepiped.
Resolving this addition of different form can be done with the same process as indicate in this above text.
Thus, we have then to add a Cube with a paralellepiped the two have a common squared face of same aeras.
More with the same method,
We can do addition between any different 3D forms because knwowing the squaring a circle method any initial form can be transformed into a cube and inversely, any cube can be transdormed into for example a sphere. Thus adding two spheres can be also easily resolved into a final resulting sphere.
Consequently, with the spatial language, it can be constructed any resulting volume of final desired form. One can get the given result from any initial different forms. The four calculation operations (Add, Sub, Mult, Div) of the spatial language are helps for doing these transformations.
With the Dakhiometry SPATIAL LANGUAGE,
1)  Manipulations of forms and volumes are easy. This is the welknown perpetual impossibility of the current millenary Mathematics due to its ignorance about the Circular properties.
2)  According to the Matter Conservation principle, any given volume can take precisely any possible forms and reciprocally.
3)  This should be a futur modern basic science method consistent with the reality fact of constructions and transformations in the nature.
Important note
There are large possibility of the Spatial Language the use of it may resolve and enlarge the horizon for the Space Science and for the universe Physics.
However, at this time The Dakhiometry Spatial LAnguage is limited in its powerful applications.
It is because spatial construction need a well precise tool according to the precisions offert by the Numeric Binary System.
A good C.A.D. is necessary for Spatial Language. The current CAD software is sufficient. However, because of the Old erroneous Pi, these software is useless for precise Constructions.
For example, the Doubling a Cube resolution need such equipment with the True universal Space Constant defined in Dakhiometry through the Squaring a Circle. It can be seen that the Doubling a Cube rests wholy on Circles definitions !!!
The current CAD software, can used in case where one need only to define Ratio. But with the Old Pi, the current CAD is useless when one need to define or to mesure precisely Length. It is because any spatial construction rest mainly on Circles figures.
The current Pi introduce error due to circles defined by the Pi=3.1416...
These are the Great Limitation in most of Spatial constructions where usage of Circles is mainly needed.
There are too much important resolutions that can not be optimally resolved when the OldPiCircle introduces systemtic errors.
Using the manual Compas is simply an awful crude tool!
From these problems,
It can be seen that sciences revival are forbiden by the current sciences by themwelves! Current Errors in sciences are by itselves producing their own Conservatism Tools.
Conservatism is never the riding master of the Rational Certainty.
 backgammon + setup (sbcglobal.net)
 Magic + The + Gathering + MYR
Any two cube volumes of side L in One volume of side [L.(2 ^{1/3})].
Comments on the results of spatial construction to resolve the Doubling a Cube.
The immediate fundamental results according to the DoublingaCube construction are:
I)  Universal laws are expressed only in TwoDimensions.
2)  The Doubling a Cube is rationally resolved by construction.
3)  The Third Root of Number 2 can be accurately constructed with the spatial language.
4)  Any quantity can be powered and reciprocally can give precisely its ThirdRoot by construction.
These are the first immediate consequences of the Dobling a Cube resolution.
It can be seen that the spatial construction gives a value of:
Starting from the average aera construction:
(40^{1/2})
Calculation are done with Numeric calculator, it is found:
(2^{1/3}) = 1.257433429...
But, directly measuring the length on the figure, it gives:
(2^{1/3}) = 1.25929868...
The different mode of measuring construction length depends to the figure precision produced by C.A.D. software. However they all are different and lesser than with the Calculation by Numbers exhaustion used in numeric calculators.
Note that this value is get from side of the double cube formula as:
2.(2^{1/3})
((40^{1/2})^{1/2})/2 = (2^{1/3})
Where (40) is the construction determined average aera.
While a calculator proceeding with Numbers calculation gives directly the value:
(2^{1/3}) = 1.259921049...
With the value of (40^{1/2}):
Spatial construction gives:
(40^{1/2}) = 6.324555320336758663...
Directly, the corresponding Numberscalculator gives:
(2^{1/3})^{8} = 6,349604207872797899...
All the differential between spatial construction and the current exhaustion algorithm method are underlined. Results of Spatial constructions are less about some 1/1000.
There are surely somme imprecision and discrepancy in the Number exhaution method when calculation are done using the current integrated different power of Root algorithms.
Important Remark
To construct the above Doubling a Cube, It is used a C.A.D. software where the integrated Pi value are the usual conventionally one as the 3.1415...
Therefore, the results that was verified with numerals given by this software, contain necessary error due to this appoximative Archimedes value.
It is why the spatial construction given by these ancient softwares are not the true exact ones. If construction use circles for measurements then, it is necessary to change the 3.14... by the new one determined by the DAkhiometry as the Space Constant, to be abble to get the accuracy of the spatial language.
It is given here
The Doubling a Cube according to
The whole spatial laguage construction method
 square + root + of + double + cube (Switzerland)
 doubling a cube animation
(comcastbusiness.net, Pittsburgh, Pennsylvania, USA)
 doubled + the + volume + of + the + cube (Turkey)
Resolution of doubling a cube is done on transformation of a given Rectangular volume into a Cube one.
It concern here to transform two unequal aeras ABCD and BCEF into two equal Squares, the two faces of the final Cube solution.
For this purpose, the two preceeding aeras are use to form the square structure for construction of the resolution.
Note that the square or the Circle structure are equivalent because these two forms are tied together.
Thus from this square structure it will be deduce the final differents diameters representing the final Doubling a Cube solution.
From this initial situation ABFECD, the final doublecube volume is:
Final cube vomume = 8 x 2
But this Final volume should be formed by two equal faces. To construct this final Cube, we will use the LamCa theorem that allows to work in the 2Dimensions and not in the 3Dimensions of a Cube.
Thus, the corresponding structure will represent the [8 x 2] in a common square denoted as the (K2) with (side=8), as shown on this next figure(a).
 doubling + the + cube + math (HMC.Edu, Harvey Mudd, Claremont, California, USA)
 how can you change the edge length of a cube so that it's volume is doubled (comcast.net, Utah, USA)
a)  It consists here to use the sides length of a parallepiped
of (8 and 2) as the side of aeras (8.8) and (2.8).
b)  Then to get their artithmetic average as:
(64 + 16)/2 = 80/2 = 40
c)  From (aera = 40), it will proceed 2 successive times the square root, starting from 40.
We get then the value of the doubled square side as:
DoublecubeSide = 2.2^{1/3}.
With this result one can get the (2^{1/3}), by divide this final cube side by (2).
To make the aeras [ABCD] and [BCEF] as equal squares, it will be constructed, not the numeralaverage, but the spatialaverage of them.
According to the LamCa theorem, it can be done the aera average not in squared lengthes but in between lengthes only.
Note that the value (MN) is no more than the Square Root of the averaging aera (S).
 cube + root (India)
OM = 2^{1/3}
Thus, the side of the final cube will be determined with the aera denoted on this next figure(c) by the [S].
a)  We have then:
SQRT(S) = R = [diameter (MN) of circle (1)]
Note that the aera {S] is in this case equal to:
[S] = 40 = (2^{1/3})^{8}
... a socalled irrational Number.
b)  Now the side solution of the final cube is given by the square Root of (MN), represented by the circle(2) diameter.
Note that the diameter (2) is here equal to:
2 . 2^{1/3}
c)  And the diameter of circle (3) will give the Exact Length value of [Third Root of 2] :
OM = 2^{1/3}
The Doubling a Cube is then solved according to the Dakhiometry Spatial Language. This solution furnishes also the rational length OM of Third Root of (2).
End of the Spatial language processing for resolving the Doubling a Cube.
 write + two + rational + and + two + errational + number + between + squar + root + 2 + bnd + squar + root + 3 (China)
 doubling the cube calculator (windstream.net, USA)
Actually, this problem is concerning calculation directly done by construction in space. It seems not clear for mathematicians because the spatial calculations is there still unknown.
In Dakhiometry all constructions use the spatial calculation method. For this purpose, there are much basis to be described and explained. But when knowing them, spatial calculations allows to resolve easily most of problems. This can not be performed by the usual complicated Algebraic rules.
It can be note that the usual results of Root calculations using Numbers given by current computers and calculators, are not excatly the same given by these spatial calculations. These latter are rationally done and should give the true values because any algebraic algorithm gives only approximative values by exhaustion.
General Conclusion
I)  One can see that the rational Dakhiometry methods has nothing to do with the whole Mathematics irrational system. This concerns as well for the Geometry than for the Algebraic systems the main error of which is to rest on the conventional pythagorean Number system.
II)  There are too much inaccurate values with the pythagorean Number calculations system and the euclidean division. Its corrections need to much mathematicians' effort and energy. Mathematics rescue is really Impossible. Mixing it with the Dakhiometry is adding to this latter a fatal contradiction.
III)  The best solution is to throw Mathematics away and for each one, to live in peace... with his conscience. This may be the "Apollo recommandation to clear for ever the plague on Earth".
When I explain how to do the Doubling a Cube and how to get wholy by construction the socalled irrational Third Root of 2 or (2^{1/3}), one will agree that:
a)  The simplicity and the efficiency of the Dakhiometry Universal Spatial Language is from an unequalled true science.
b)  The Mathematics Impossibility and its Irrational Numbers are from man of the Neolithic Age.
Would you like that one day in the futur, some Greenman will qualify the earthling like that?
What is the generalisation of Doubling a Cube?
The Doublibg a Cube is in fact an Impossible problem of Mathematics. However, it is really a simplistic one.
The Dakhiometry had established the necessary laws for Doubling:
A sphere,
A cone,
A cyclinder,
A pyramide,
...
And more complexe forms as:
An ellipsoïdal one
A paraboloïdal solid,
A hyperboloïdal one,...
What are the necessary laws thet let to such transformations?
1)  It is to know what is the volume or structure of matter in space.
2)  To know what is the absolute space Transformation capability.
What is the meaning of the DoublingaCube generalization?
 principle + of + enlargement + objet (Malaysia)
Enlargement and decreasisng object are from principle of the Volume Transformation in space.
The Doubling a cube generalization has two aspects.
With (L) as the side of an aera and according to the above two aeras (ABCD) and (BCEF), two faces of representing an initial volume form, it can be defined its final transformation into Cube by the following equation:
[(L.L).n)].L
where (n) is a multiplication factor as well as a division one.
Therefore,
A)  With (n) fixed, this equation can vary according to (L), the side of any cube.
B)  With a (L) fixed, then we get the equation of any (n) as [n^{1/3}].
a)  Case (A) means that cubic volume multiplication and division is allowed for any cube dimension.
b)  Case (B) means that the Root3 [n^{1/3}] of any quantity (n) is constructible. There is no "irrational Number".
Irrational is Mathematics fantasy is harmfull for all the current sciences.
General conclusion of the Doucling a Cube resolution
There are vast consequences from the resolution for a simplistic Mathematics Impossibility of the "DOUBLING A CUBE".
This means that
Knowledge of MATTER, with its laws and principles, are unfathomable lacks of Mathematics.
Example of the doubling a cube is to see what is the wealth of the Dakhiometry Absolute Space.
Thus the poor Number formalism is that:
when one write (x^{3}), it has no real meaning as does any formalism.
Here with the spatial language a cube can be written as:
[(L.L.n).L]
But also,
[(L1.L2.n).L3]
With the spatial language:
1)  From there one can see as for in 2dimensions, it can be get a square aera under any other form of a same aera and inversely.
2)  In the same manner, with the Spatial Language and in 3dimension, any cubic volume can be trasformed in any other same volume forms else than the Cubic one and inversely.
3)  It can be done simply and directly Multiplication and Division of volumes.
For example, it can be done the Cubing a Sphere and inversely. This concerns also for transmuting forms in another ones on their volume criterion. Morphing becomes precise and easy.
Mastering the spatial language gives rise not only to enlarge knowledge but also to the wealth of practical possibilities.
Mystery when adding Numbers Ideology
to practical manipulation with usual object Forms
 découverte + de + la + propriété + de + Pithagore + au + Congo (Germany)
 definition + of + impotence (United Arab Emirates)
 formalist + model + of + language (Australia)
Actually.
In practices, twoadded tiles aeras can be practically verified as equal to one bigger squares aera. This statement can be verified for any tiles aeras... but only as the particulat form of practical tiles.
Euclide also did not perform a proof but a means to verify this equality for any square dimensions. But he succeeded to verify it because he used a figure based on the structure Square/Circle. However this structure was not yet undestood by himself.
 Pythagorean + Theorem + jokes (east.verizon.net)
 Pythagoras + theorem + joke (bhn.net)
It is because a theorem needs to be deduced from some anterior reason that allows the existence of some recognized property.
It is the case of the Pythagorean about summation of squares. This theorem is then a formalism from language that may be:
"Two squaretiles is equal to one Bigger squarretile... whatever the dimension of these "square tiles".
This is as from a proverb or a prophecy but not a rational reason.
The next following riddle shows that the Pytahgorean proverbtheorem is not verifyed for any case.
While the Dakhiometry Lamca theorem is a general law expression of the universe space structure between two fondamental forms as the SquareCircle.
1)  Therefore, the Pythagoras's theorem cannot be proved by Homothetic manner to be generalized.
2)  While the Lamca theorem is a basic theorem founded on the properties of the universal structure Square/Circle. It is why the homothetie is there not a proof but can be used as a consequence for an extended view... only when it rests on the Lamca proof. This is an important point for understanding the wealthy LamCa theorem. This latter is then wholy and fondamentally different from the welknown pythagorean theorem.
Exemple for understanding the Homothetie
A)  A ratio and homothetie of numbers or of lengths is only a relativity view point that define nothing uniquely. Only is indicate there the ratiorepetition.
B)  Homothetie from only a rational proved theorem is the valid universal expression of this theorem.
Here next is a corresponding figure expressing this difference.
Another example of dummy bad theorem:
a)  Bad Theorem on Day event: "The Day is the Sun all along the Time conqueror over the Night". This interpretation is originated and corresponding to a repetive relativity mechanism.
b)  Good corresponding theorem: "The Day and the Night is due to the Earth property of being a globe as a conservative structure". This is a theorem based on absolute reason from the universal circular property.
It is why when not resting on rational proof the pytahgorean theorem is not the result of a rational proof event if it is verified in particular figure cases.
It is the case of the "Thales thoerem" which is only a mechanical repoduction of a Ratio, even if it is verifyed, is not a rational proved theorem.
It is differently for the LamCa theorem, where it rests on the foundation of the proved Universal Square/Circle structure. Therefore, the LamCa theorem can be expressed under its particular aspect as a Ratio.
This was used by the Dakhiometry to prove:
the universality of these next formula:
x^{2} + y^{2} = y^{2}
using separately the Thales theorem for each member.
Or as figures for squares calculation:
Square1 + square2 = square3
Or more extended:
Aera1 + aera2 = area3
Also using separately the Thales theorem for each member...
where the homothetie is not there an internal operation of the formula... because The homothetie is used here to underline the presence of the universal Square/Circle structure. It shows here the constantancy presence of a universal reason.
In the case of the above Pythagorean theorem figure, applying the homotheic operation is only an artificial mechanical operation for repetition of the ratio that add no more definition than the same ratio for mechanical repetition.
The following pytahgorean eqalities is only verifyed by the euclidean Mechanism of Supperposition.
A Mechanism is not a ratonal argument to introduce the necessary generality for a real theorem.
Because a mechanism is a practical means "to verify". It signification is that one can never verify the summation certainty of Two Square Aeras as big as the Sun scale Dimension for example!
It is why:
A verification is never an rational argument on that a theorem should be founded !!!
For example the Platoo's Compas is a mechanism that never be something like a True Rational and wealthy Definition for Circle property.
The Anciants and Modern mathematicians that never know what is the Angle Trisection solution indicate this Circle Ignorance despite this welknown Platoo's Compas.
In summary:
A Vérification that is only a Practical Mechanism should be never a rational Argument for a universal Law.
The Euclide "Equality By Supperposition" is only from an Anciant's prophetical law.
This riddle on Squares Summation shows that one can never perform the Mechanism of the pythagorean theorem when the practical condition cannot be accessed as the Sun scale and more for example.
What is the impotence of the Numbers formalism system? Here is following a diagram as a riddle that tells it to you:
... at aeras at the Sun scale for example...
One should be in conscience that the help of the Thales's Theorem is an another illusion because a Ratio is a Mechanism that don't tell nothing about the certainty of Equality Mechanisms at the Sun scale for example... for axample when you are working with the Einstein Relativities.
One should be in conscience that equality and ratio should rest necessary on the Proof that the Universe Space is Absolute.
So what Mathematicians and Einstein have to do with the Thales Theorem and the Equality when they believe to the Nothingness and to the Noformed Relativityspace in their Unformed universes!
You have to complete this above series of Number meaning.
In fact, the Pythagoras and Socrate theory is only valid for the first terms of squared Numbers (L).
 Pythagoras + theorem (South Africa)
 ancient art root rectangle (bellsouth.net, Jacksonville, Florida, USA)
 compress + and + straightedge + construction + golden + rectangle (adelphia.net, USA)
 tarememe + de + Pythagore (Belgium)
 théorème de Pythagore expliqué aux enfants (Germany)
En réalité c'est ce que d'origine, les bâtisseurs de monuments savent par pratique. Et surtout c'est ce que les Anciens mathématiciens avient reçu de ces artisans comme expériences. Les careleurs des palais, doivent savoir ces figures sur le bout des doigts. C'est que les careleurs, pour bien réaliser des figures avec des carreaux de mosaïque, ils doivent découper les carrés de carreaux en plus petit et de formes variées pour réaliser en même temps un parquet bien plate et lisse mais aussi, pour y faire apparaître des figures magnifiques. Aussi, ils doivent savoir par expérience, ce qu'est la fameuse relation que plus tard on l'attribuait par abus, à Pythagore parce que c'était un grand parleur. Comme on le sait, on se valorise plus en disant que c'était la découverte d'un Grand penseur...
 pythagoras + golden + ratio (Thailand)
Example of the Golden Triangle.
Origin of the socalled golden cube is from Spatial considerations and not due to some mystic Numbers.
 montage + étagère + multicube (PointeàPitre, Guadeloupe)
Oui, étagère, fenêtres, balcons,... ect, en triangled'or.
 the + problem + of + thales + about + magic + triangle (Philippines)
 how + do + we + use + pythagoras + theorem + in + everyday + life (South Africa)
 who + uses + pythagorean + theorem + meme (..)
 Golden objects of cult of Rome (Russian Federation)
 doubling + cube (sbcglobal.net, Missouri)
 Pythagorean + Theorem + by + Homothetic + Copies (..)
An homothetie figure is only a RATIO.
Therefore, a ratio is not a reason. It express only a relativity.
Specifying a "ratio oe a Relativity" is not a Reason to use as a proof. An homothetie is valid only when it is used as a figure to express the universality of a reason.
Therefore, the Dakhiometry LamCa theorem to prove the summation of aeras, can be expressed the universal certainty" that is initially proved.
Because the pythagorean is only verified but nevr be proved, we can't assert that an homothetic figure of a figure is actually a valid rational and proving argument.
Here is: x^{2} + y^{2} = k^{2}
Where golden Length (k) is:
k = 6.4031242374... as a rational space Length.
 how + to + do + the + thero + de + Pytagore (yk.ca, Canada)
En effet.
C'est vraiment du "théo" ou du dzero.
 formation + of + cubism (rr.com, North Carolina, USA)
 Architecture pythagorean theorem word problems (USA)
 formule + mathematique + integrale (Nice, France)
The Number formalism is nill:
x^{2},
x^{3}
x^{n}
x^{2}+y^{2},
...
What pythagoras and then, Fermat and other mathematicians can see through theses Numbers?
 What the Mathematics does with
its belief on the Pythagores' Number ideology?
Here next, are two examples of the Dakhiometry capacity of Volume manipulations.
Examples of the Dakhiometry "GOLDEN SPHERE" and "GOLDEN CONE".
 matter + transformation + and + the + universe (comcast.net, Indiana, USA)
Even if any universal laws expressed in twodimensions, Transformation in the universe space are done in threedimensions. With the spatial language, it can be donne precisely the transforming of any volume of matter. The volume of matter should be seen as being in two and also three dimension forms.
The Dakhiometry can transform 3D volumes of diffrent solid forms by adding, substracting multiplying and dividing directly any basic solid volume.
These laws are rationally proved and rest on the fundamental properties of the Universe Absolute Space.
 transmutation + circles + and + their + meanings (sbcglobal.net, LosAngeles, USA)
The transmutation circles is strongly tied with all that, the consequences of which is as vast as the universe space.
Joke Definition (australia).
 The + Pythagorean + Cube (Australia)
Actually, certaintly and surely.
From the circle was born the Square. From the Square was built the Cube. Finally, from the Cube was solidly related any other forms. From there the universe construction is done.
 doubling of the cube solution (Belgium)
The given spatial construction is a rational and precise one. The difference in results with the current number calculations are from some (10^{3}). It is significantly relative to the current exhaustion algotithm method used in Root Number calculation.
Actually, the above description for the Doubling a Cube problem is really a joke. It consists how to complicate any problem resolution even with spatial construction method.
I suggest you to donot lose too much time to the above given constructions.
However, the above constructions are exercices that shows how the spatial construction allows a first approach of the Doubling a Cube problem.
The true Dakhiometry Doubling a Cube
A high level of spatial Construction
For resolving the Doubling a Cube and more fundamental problems in Space.
It will be soon exposed in this page the different rational however "magic" construction methods:
A)  How to obtain any (n) power degree of a given length Quantity. B)  Inversely, how to resolve (n)th Root of any length Quantity by construction.
In spatial construction, (n) is a LENGTH the precise Quantity in the universe.
Particularly,
The Doubling a Cube is resolved precisely when understanding how to get FROM a Length (L) the (L)^{n)} one. And inversely,
how to get (L) from a given (L)^{n)}.
Here,
Doubling a Cube of side (L) is to resolve the final side of a Cube_{(f)} solution as,:
Cube_{(f)} = (L).2^{1/3}
Therefore, the doubling any side (L) of an initial Cube is to defined what is the Length Quantity third Root of 2:
2^{1/3}
As the method allows how to define any (x)^{1/n} then,
1)  The multiplication of any cube volume with side (x) can be resolved easily in Dakhiometry from a given Multiplying (n) degree root.
2)  Reciprocally,
How from a cube side (n) in (n)^{1/x},
It can be determined its Dividing root factor (x).
This is the Dalhiometry law of Multiplying and Dividing a cube volume, never known or Impossible one in Mathematics. More, it is extended to any derived another volume form.
This law has a wealthy consequences for human's science on the universe MORPHING OF OBJECT VOLUME or how to give a determined FORM to an initial object.
> Extraterrestrial greenman's law, isn't?
