The 'hyperbolic sine' of a sphere [Le 'sinus hyperbolique' 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' = sinh(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):


exponential
cosine
sine
tangent
hyperbolic cosine
hyperbolic sine
hyperbolic tangent


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


exponential
cosine
sine
tangent
hyperbolic cosine
hyperbolic sine
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:




(CMAP28 WWW site: this page was created on 06/10/2022 and last updated on 08/13/2022 13:35:51 -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 to AVirtualMachineForExploringSpaceTimeAndBeyond [Retour à AVirtualMachineForExploringSpaceTimeAndBeyond]]

[The Y2K Bug [Le bug de l'an 2000]]

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


Copyright © Jean-François Colonna, 2022-2022.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2022-2022.