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.
"Octahedral Globe from a Window," by Frank A. Farris, Santa Clara University, CA
Ink jet on paper, 2015.
This coloring of the sphere, based on a photograph of a stained-glass window by Hans Schepker, is invariant under the action of the octahedral group. I created it by mapping the sphere (and the group action) to the plane via stereographic projection and using known techniques for creating complex-valued functions invariant under groups that act on the plane. This image is part of a larger work, "Imaginary Planets." --- Frank Farris