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.
"Ball and Chain," by George Hart (Museum of Mathematics, New York, NY)
Nylon (selective laser sintering), 6" x 6" x 6", 2009
Ball and Chain is a ball made of triangular chain mail mesh containing twelve flexible regions in a rigid dodecahedral framework. There are 3,722 small rings, which interlock to form a sphere with chiral icosahedral symmetry. At 920 places, six triangles meet, but at 12 special points (at the center of the twelve dimples) only five triangles meet. The ball does not collapse down to a disk because the dodecahedral structure of ribs (made by having some of the rings lock to form a skeleton) is rigid. But in twelve circular regions the rings are free to hang freely. No matter how it is turned, the top six regions hang to make concavities while the lower six regions are convex and blend in with the overall spherical form. The complete structure was created as one unit in its assembled state by selective laser sintering. --- George Hart (http://www.georgehart.com)