Absztrakt:

A new attempt to develop a dynamic geometry by means of digital 3D animation for hitherto abstract higher dimensional mathematical concepts in order to visualize quantum phenomena as performed during the QUANTUM CINEMA-project in Vienna shall be introduced. The virtual space model based on a 5D lattice for the visualization of continuous transformations of algebraic descriptions opens a field for discussions: is this hyper-Euclidean approach appropriate for the depiction of non-Euclidean geometries, c.f. Hyperbolic geometry, Minkowski space and Riemannian manifolds? Also some assumptions for visualization of complex numbers, and the imaginary factor of time in the same framework will be discussed. Furthermore some new visualizations of higher dimensional space configurations shall be presented: Two newly found golden heptahedra, named epitahedra (E±) can be assigned as 3D representations of Penrose kites and darts tilings which is known as slice of the 5-dimensionale space. These polyhedra may serve as visualization tool for group theoretic descriptions, which should be further developed for modeling quantum phenomena as an occurrence of space itself. Finally 3D animated movies of the 5-dimensional space reveal the kaleidoscopic symmetries of the Poincaré dodecahedral space which seems to be only visually accessible with epitahedra, those unit cells which even could be identified as Plato’s 5th elements constituting his world of ideas.