Action LogoThe dakhiometry

L'évolution de l'univers

Nguyên Tân Tài

Squaring Circle









Dakhiometry
MULTIPLYING THE VOLUME OF A CUBE

Its consequences.







Adding Cubes


by Nguyên Tân Tài


Construction Law of Viêt-Nam












How to MULTIPLY A CUBE VOLUME.
The consequences of its resolution.








- angle + trisection + best + results + 2011 (Egypt)

a) -In the meantime, the meaning of doubling-a-cube 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 Doubling-a-Cube 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 (21/3) is a false statement that rests on a false argument statement as due to the irrational (21/3). It is proved in this texte with the complete resolution of the Doubling a Cube conjecture where the (21/3 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 doubling-cube 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)

- 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 Three-Dimensions 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:

Doubling-a-Cube = 2.(Cube-side)3
or
Solution of final Cube-Side = (cube-side).((21/3))

Mathematicians will get and another doubt following the doubling-a-cube one. This is the new doubt about:

Is ((21/3)) 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



- 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 X3

Now, this cube-side will be 2.X

The final resuling cube volume will be:

(2.X)3

But not as a double cubes like,
2.(X3)

- 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.


Double cubes

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 Trans-Forms.



- 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 3-dimensions 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 Black-Hole 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 TWO-DIMENSIONS.

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 3-dimensions 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 (2-unités 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 Sgnifié-Et-Signifiant, 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 connaître-ce-que-l'on-est-capable-de-connaître. 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 est-elle 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 Même-Figure 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'unité-de-longueur-donnée, est NECESSAIREMENT VRAI POUR TOUTE autre échelle de DIMENSION car, UNE STRUCTURE DE L'ESPACE EST DANS LA PERMANENCE, VRAIE.
Pour quelle Raison peut-on 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, fusse-t-elle 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 2-unité, 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 Site-ci 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 quatre-unités 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 adjacent-cube 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 Lam-Ca theorem.
Thus for the final Cube solution we have to work its volume on the base of this two initial un-equal faces (ABCD) and (BCEF) as shwon on this next figure.

Transforming into Cube

Transforming polygonal form into Cube one.



This is the Dakhiometry principle of the Doubling-a-Cube 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 so-called Pi for this Doubling-a-Cube, is the Dakhiometry one.
If you use your old Archimedes' Pi, this problem can never be resolve and the (21/3) 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 DOUBLING-A-CUBE WAS EASILY RESOLVED WHOLY OWING TO THE DAKHIOMETRY LAM-CA THEOREM




All the steps of constituing the Doubling-a-Cube 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.

Doubling cube resolution

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 Circle-to-Square transformation, one cannot resolve the Square-to-Square 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 cercle-carré 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 mean-time, this Space Constant is denoted simply with the currently use as the "Pi". The Spatial Constant is given by this numeral formula:

Pi Space Constance

The space constant has nothing to do with the "Pi-meter" 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 Lam-Ca theorem, which is not a simplistic summation of to squared conventional Numbers. The Lam-Ca theorem is a pass for travelling throughtout the universe Space for transforming aeras and volumes of matter.

Note that the Doubling-a-Cube resolution is no more than simply, the direct result of the Lam-Ca 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 resolution

Construction for Doubling a Cube


Steps of construction

One know how to calculate a circle aera (S) with the diameter (D):
S = (Pi/4).D2
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 = (42.Pi/4)

K2 = (82.Pi/4)

Then:
aera (1) = K1+(K2-K1)/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) = ((21/3))8

2) - Circle (2) diameter is:
Diameter circle (2) = ((21/3))4

3) - Circle (3) diameter is:
Diameter circle (3) = ((21/3))2

4) - Finaly, the square root of Circle (3) diameter is:

Square Root of diameter (3) = ((21/3))


The Doubling Cube solution is given by the circle (2) diameter.

Diameter circle (2) = 2 . ((21/3))

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



Doubling a Cube proof

Different construction steps for Doubling a Cube

This animated gif resumes the different steps
to construct the Doubling-a-Cube.



- 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.









NOTE


All these above calculations can be performed entirely and precisely with the Dakhiometry spatial language.

This means that the (21/3) 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 (x1/3) by constructions, without finding Irrational Nothingness.


Generalization of Cubic-Transformation

Cubic-transformation is denoted for transformations Cubes into Cubes.

The Doubling a Cube is only a particular case.
Generalization of cubic-transformations can be extended as Cubic Multiplication and Division.



- 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 3-D 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.











Doubling cube resolution

Any two cube volumes of side L in One volume of side [L.(21/3)].








Comments on the results of spatial construction to resolve the Doubling a Cube.




The immediate fundamental results according to the Doubling-a-Cube construction are:

I) - Universal laws are expressed only in Two-Dimensions.

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 Third-Root 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:
(401/2)

Calculation are done with Numeric calculator, it is found:

(21/3) = 1.257433429...

But, directly measuring the length on the figure, it gives:

(21/3) = 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.(21/3)

((401/2)1/2)/2 = (21/3)

Where (40) is the construction determined average aera.

While a calculator proceeding with Numbers calculation gives directly the value:

(21/3) = 1.259921049...



With the value of (401/2):

Spatial construction gives:

(401/2) = 6.324555320336758663...

Directly, the corresponding Numbers-calculator gives:

(21/3)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)




The Pythagoras secret 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 double-cube 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 Lam-Ca theorem that allows to work in the 2-Dimensions and not in the 3-Dimensions 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:
Double-cube-Side = 2.21/3.

With this result one can get the (21/3), by divide this final cube side by (2).



Solution of Doubling-a-Cube

To make the aeras [ABCD] and [BCEF] as equal squares, it will be constructed, not the numeral-average, but the spatial-average of them.
According to the Lam-Ca theorem, it can be done the aera average not in squared lengthes but in between lengthes only.

Solution of Doubling-a-Cube

Note that the value (MN) is no more than the Square Root of the averaging aera (S).



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 = (21/3)8
... a so-called 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 . 21/3

c) - And the diameter of circle (3) will give the Exact Length value of [Third Root of 2] :
OM = 21/3


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 so-called irrational Third Root of 2 or (21/3), 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 Green-man 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 Doubling-a-Cube 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 [n1/3].

a) - Case (A) means that cubic volume multiplication and division is allowed for any cube dimension.
b) - Case (B) means that the Root3 [n1/3] 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 (x3), 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 2-dimensions, 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 3-dimension, 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)





What is the impotence of the Numbers formalism system? Here is following a diagram as a riddle tells it to you:

The Pythagoras secret

You have to complete this above series of Number meaning.
In fact, the Pythagoras and Socrate theory is only valid for the first term 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)



Golden Cube cult

Example of the Golden Triangle.

Origin of the so-called golden cube is from Spatial considerations and not due to some mystic Numbers.



- montage + étagère + multicube (Pointe-à-Pitre, Guadeloupe)

Oui, étagère, fenêtres, balcons,... ect, en triangle-d'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)




Golden Cube cult




Here is: x2 + y2 = k2

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:

x2,
x3
xn
x2+y2,
...

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 two-dimensions, Transformation in the universe space are done in three-dimensions. With the spatial language, it can be donne precisely the trans-forming of any volume of matter. The volume of matter should be seen as being in two and also three dimension forms.


The Pythagoras secret

The Dakhiometry can transform 3-D 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, Los-Angeles, 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).21/3

Therefore, the doubling any side (L) of an initial Cube is to defined what is the Length Quantity third Root of 2:
21/3

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.

--->       Extra-terrestrial green-man's law, isn't?
































Hereafter are texts on the Dakhiometry,
a rational method for determining properties of the dakhi, the Breath of the universe ...


The dakhiometry, text DK001EN   (sep 2001) The Simultaneity and the Conservation are notions of the Permanence of the universe.
The dakhiometry, text DK002EN   (oct 2001) The memory-universe built in respect of rigorous conditions, but with simplicity.
The fundamental concepts in the Dakhiometry  (nov 2001) In dakhiometry, universal laws and phenomena show surprising wealthy relationships. The future physical Laws are not yet established in the universe of nowadays.

The Accuracy, the Certainty and the Doubt  (nov 2001) Mathematical accuracy is a mechanical process while Certainty and Doubt are the engine of the evolving Self. Some analysis of the Non Euclidean contradictions.

Proof of the Fermet's theorem  (mars 2002) Equation xn+yn=zn, has no solution....

Cyclone formations  (mai 2002) Cyclones are phenomena attached to the band structure of the atmosphere winds....

The First action of the beginning of the universe  (sept 2002) How to square a circle. This surface transformation is the first natural operation at the beginning of the universe....

The Proof of the universe Evolution Process  (oct, 2002) The beginning of the universe construction used the squaring a circle to allows the central symmetry to establish the left-right symmetry for the alive.

The Proof of the squaring a circle  (oct, 2002) Proof of the surface equality after the squaring a circle.

The basics of Matter. The proof of Thales' theorem. The proof of the Pythagoras' theorem.   (oct, 2002) Properties of Matter allows to state some foundations on the knowledge. From these bases, simple proof can be done one the Thales' and the Pythagoras' theorems.

The Archimedes' Property  (jan, 2003) The Archimedes' property was used by the resolution of the circle perimeter that was attributed to Archimedes. Analysis are done on this resolution. This axiom is very used in modern mathematics and some confusion are commented.

New Proof of Light Refraction and Reflection Laws  (dec, 2004) New Proof according to the Dakhiometry method that shows that light is not a particle and a wawe that may have a trip of 13 billion of celerity distance...

New Proof of Light Refraction and Reflection Laws  (dec, 2004) New Proof according to the Dakhiometry method that shows that light is not a particle and a wawe that may have a trip of 13 billion of celerity distance...

Properties of circular structures and their consequences.  (jul, 2005) This page introduces the contents of a work that constitutes the foundation of the Dakhiometry...

Liquid Archimedes' property an the Potential as gravity.  (jul, 2005) Statement on Liquid proerties and object Potential energy as the consequences of the condensed matter process localisations...

Archimedes' gravity center volume measurement method.  (dec, 2006) Proofs of solid aeras and volumes measurements, was all unsuccessfully done and quite erroneous works...

Unbounded Energy Source Engine (In French)
"Le Moteur Source d'Energie de tous les temps"
 
(Aug, 2006)
An application of the liquid law new understanding to build a machine producing energy of high capacity. A reality for the near futur.

Succession allows Quantities. Basic of Counting.   (august 2007) Unity Succession Principle is the foundation of the universe Fullness. fullness is necessarry to allow Quantity. Quantity is Reality of the World existence.

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





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




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