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.
"Stereographic projection (grid)," by Henry Segerman (Oklahoma State University, Stillwater)
3D printed nylon plastic, lamp, 10 x 9 x 9 cm, 2014
The light rays from the lamp are partly blocked by the shrinking design on the sphere; the resulting shadow is a regular tiling of the plane by squares. This illustrates how stereographic projection transforms the sphere, minus the north pole, into the plane. Note how shapes are slightly distorted near the south pole, and dramatically distorted near the north pole. --- Henry Segerman