The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"Double Boy Klein Bottle," by Carlo Séquin (University of Califnornia, Berkeley)
6" x 8" x 7", FDM Model (blue ABS plastic), 2012
Boy's surface, a compact model of the projective plane, with a small disk removed is topologically equivalent to a Möbius band. Every Klein bottle can be composed of two Möbius bands that are glued together by their edges. In this model a Klein bottle is created by gluing together two mirror images of a 3-fold symmetrical Boy surface with a disk removed from its pole. The result is a Klein bottle with S6 symmetry, showing six of the "inverted sock" openings characteristic of the classical Klein bottle. -- Carlo Séquin