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 eight knot," copyright Andrew Lipson. Made of Lego ®
I think this is the most difficult single construction I have ever made out of Lego®. Those long sweeping curves, hanging unsupported in space... It's only when you get about 2/3 of the way up that you start to discover exactly which bits 1/3 of the way up aren't strong enough. And there are never enough 1x3 bricks... But I didn't cheat anywhere. The figure-eight knot has a nice tetrahedral skew-symmetry which the model illustrates quite well. On my website you can find more pictures and an LDRAW .DAT file generated by my program for this sculpture. Beware--the .DAT file builds it out of 1x1 bricks. Actually constructing this out of larger bricks so that it holds together is a (non-trivial) exercise! Lego® is a trademark of The Lego Group. --- Andrew Lipson (http://www.andrewlipson.com/mathlego.htm)