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.
"Lawson's Minimum-Energy Klein Bottle," by Carlo Séquin (University of California, Berkeley)
9" x 6" x 4.5", FDM model, 2011 Third Place Award, 2012 Mathematical Art Exhibition
My professional work in computer graphics and geometric design has also provided a bridge to the world of art. This is a gridded model of a Klein bottle (Euler characteristic 0, genus 2) with the minimal possible total surface bending energy. This energy is calculated as the surface integral over mean curvature squared. --- Carlo Séquin (University of California, Berkeley, CA, http://www.cs.berkeley.edu/~sequin/