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.
"Ovoid Bead with three Hyperbolic Axes as a Lamp," by Gabriele Meyer (University of Wisconsin, Madison)
I like to crochet hyperbolic surfaces. This object started as a hollow ovoid, top and bottom missing. I then crocheted three vertical axes down the sides. These three axes are the basis for the hyperbolic crochet. The object is hung from the ceiling.
I then entered a light tube. The photograph was taken in the dark without flash. --- Gabriele Meyer