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.
"Hyperbolic Cube," by Thomas C. Hull (Western New England College, Springfield, MA)
Single sheet of Canford paper, wet-folded, 9" x 9" x 9", 2006. A Hamilton cycle on the cube has eight edges. Therefore, a regular octagon could be folded to mimic the path such a cycle traces on the cube. This piece represents a solution using folded concentric octagons, producing the illusion (?) of negative curvature. The piece was folded from a large regular octagon, approximately two feet in diameter. Concentric octagons were pre-creased, alternating mountain and valley folds. Then the model was collapsed and wet-folded to hold the cube Hamilton cycle shape. "I've been practicing origami almost as long as I've been doing math. Part of the charm of paper folding is its capacity for simple, elegant beauty as well as stunning complexity, all within the same set of constraints. This mirrors the appeal of mathematics quite well. Geometric origami, which is where most of my artwork lives, strives to express in physical form the inherent beauty of mathematical concepts in geometry, algebra, and combinatorics. The constraints that origami provides (only folding, no cutting, and either one sheet of paper or further constraints if more than one sheet is allowed) challenges the artist in a way similar to being challenged by a mathematical problem." --- Thomas C. Hull (Western New England College, Springfield, MA) http://mars.wnec.edu/~thull