Tridimensional representation of a quadridimensional Calabi-Yau manifold [Représentation tridimensionnelle d'une variété quadridimensionnelle de Calabi-Yau ]

Tridimensional representation of a quadridimensional Calabi-Yau manifold [Représentation tridimensionnelle d'une variété quadridimensionnelle de Calabi-Yau].




Au début du vingtième siècle, deux théories sont venues bouleverser notre vision de la Réalité: la Mécanique Quantique et la Relativité Générale. Elles permettent de décrire, avec une précision étonnante, respectivement les plus petites et les plus grandes structures de l'Univers. Mais à ce jour (et c'est-là le grand défi auquel sont confrontés les théoriciens à l'aube du vingt-et-unième siècle), elles restent inconciliables, or le Graal du physicien est l'unification. Une approche prometteuse, mais encore fortement hypothétique, est celle dite des supercordes dans laquelle les particules élémentaires ne seraient plus ponctuelles, mais monodimensionnelles. Pour assurer sa cohérence mathématique, elle exige que l'espace-temps possède 6, voire 7, dimensions supplémentaires. Celles-ci nous sont évidemment invisibles, une explication possible en étant qu'elles seraient infinitésimales et "enroulées" sur elles-mêmes de façon fort complexe, décrite par les variétés de Calabi-Yau dont est présentée ici, de façon "artistique", une section tridimensionnelle dans l'une d'elle. Une analogie permet de mieux comprendre cela: un cylindre (une surface bidimensionnelle) vu de très loin semble être une ligne droite (monodimensionnelle), mais en s'en rapprochant on voit qu'en chacun des points de cette dernière il y a un cercle qui lui est orthogonal.


See its evolution:

Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold


See its 5x5=25 patches:

The 5x5=25 patches of the tridimensional representation of a quadridimensional Calabi-Yau manifold The 5x5=25 patches of the tridimensional representation of a quadridimensional Calabi-Yau manifold


See its rotation:

Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold


See some sets of 4x3 stereograms:

Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms


See an anaglyph:

Anaglyph -blue=right, red=left- of a tridimensional representation of a quadridimensional Calabi-Yau manifold


See the Calabi-Yau manifold:

Tridimensional representation of a quadridimensional Calabi-Yau manifold


See the familiar tridimensional space:

Tridimensional representation of our familiar tridimensional space


See a simple analogy regarding the so-called compact extra space dimensions:

3 D ==> 10 D:
Tridimensional representation of our familiar tridimensional space Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-

1 D ==> 2 D:
A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance? A cylinder -a bidimensional manifold-


See some related pictures (possibly including this one):

Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?- Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?- Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?- Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-  
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space- Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space- Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space- Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-


See a set of 4x3 stereograms:

Rotation about the Y (vertical)axis of a tridimensional representation of quadridimensional Calabi-Yau manifolds that can also be viewed as a set of 4x3 stereograms -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-


See some related fractal objects:

Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 4- Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 4- Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5- Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-  
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold  
The intersection of the Menger Sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation- The intersection of the Menger Sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation- The intersection of the Menger Sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation-


See some artistic views:

Artistic view of a quadridimensional Calabi-Yau manifold Artistic view of a quadridimensional Calabi-Yau manifold Artistic view of a quadridimensional Calabi-Yau manifold  
Tridimensional representation of a quadridimensional Calabi-Yau manifold A truncated quadrimensional Calabi-Yau manifold with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-  
Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of one of the 2339 pentominos 6x10 puzzle


This manifold was computed with the following parameters: 
                    n  = n  = 5
                     1    2



                    A = B = 1
[See the equations of this quadridimensional Calabi-Yau manifold]


See some related pictures (including this one) about picture sharpening:

Tridimensional representation of a quadridimensional Calabi-Yau manifold Tridimensional representation of a quadridimensional Calabi-Yau manifold -picture sharpening- Tridimensional representation of a quadridimensional Calabi-Yau manifold -picture sharpening-


(CMAP28 WWW site: this page was created on 02/14/2005 and last updated on 06/04/2026 22:23:26 -CEST-)



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