The 'exponential' of a sphere [L''exponentielle' d'une sphère ]

The 'exponential' of a sphere [L''exponentielle' d'une sphère].




A tridimensional object is defined as a set of points P={X,Y,Z}. To each point P is associated the following pseudo-octonion O={X,Y,Z,0,0,0,0,0}. Then each pseudo-octonion O is submitted to the transformation: 
                    
                    O --> O' = exp(O)


At last a new point P' is defined with {X',Y',Z'} being arbitrary linear combinations of the components of O'. The set of points P' defines a new tridimensional object...


See some related pictures using octonions (possibly including this one):

The 'exponential' of a sphere
exponential		The 'cosine' of a sphere
cosine		The 'sine' of a sphere
sine		The 'tangent' of a sphere
tangent		The 'hyperbolic cosine' of a sphere
hyperbolic cosine		The 'hyperbolic sine' of a sphere
hyperbolic sine		The 'hyperbolic tangent' of a sphere
hyperbolic tangent


See some related pictures using pseudo-octonions (possibly including this one):

The 'exponential' of a sphere
exponential		The 'cosine' of a sphere
cosine		The 'sine' of a sphere
sine		The 'tangent' of a sphere
tangent		The 'hyperbolic cosine' of a sphere
hyperbolic cosine		The 'hyperbolic sine' of a sphere
hyperbolic sine		The 'hyperbolic tangent' of a sphere
hyperbolic tangent


Nota: the radius and the colors of each particle visualizing a point P' vary according to its {X',Y',Z'} coordinates...


See a related picture:

A sphere -positive curvature-


(CMAP28 WWW site: this page was created on 06/10/2022 and last updated on 06/04/2026 23:38:32 -CEST-)



[See the generator of this picture [Voir le générateur de cette image]]

[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[Please visit the related GeneralitiesVisualization picture gallery [Visitez la galerie d'images GeneralitiesVisualization associée]]
[Please visit the related NumberTheory picture gallery [Visitez la galerie d'images NumberTheory associée]]

[Go back toMathematics - A Virtual Instrument For Exploring Space Time And Beyond [Retour à {a chapter of 'Mathematics-AVirtualInstrumentForExploringSpaceTimeAndBeyond'}]]

[The Y2K Bug [Le bug de l'an 2000]]
[Are we ready for the Year 2038 [Notre informatique est-elle prête pour l'An 2038]?]

[Site Map and Help [Plan du Site et Aide]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]


Copyright © Jean-François COLONNA, 2022-2026.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2022-2026.