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.
"Figure-8 Knot," by Carlo H. Sequin, University of California, Berkeley (2007)
Second Prize, 2009 Mathematical Art Exhibit. Bronze, 9" tall. "The Figure-8 Knot is the second simplest knot, which can be drawn in the plane with as few as four crossings. When embedded in 3D space it makes a nice constructivist sculpture. This particular realization has been modeled as a B-spline along which a crescent-shaped cross section has been swept. The orientation of the cross section has been chosen to form a continuous surface of negative Gaussian curvature." --- Carlo H. Sequin, Professor of Computer Science, EECS Computer Science Division, University of California, Berkeley