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.
"Natural Cycles," by Erik Demaine (Massachusetts Institute of Technology) and Martin Demaine (Massachusetts Institute of Technology, Cambridge, MA)
Elephant hide paper, 9"x9"x9", 2009. The sculpture is a modular combination of three interacting pieces. Each piece is folded by hand from a circle of paper, using a compass to score the creases and cut out a central hole.This transformation of flat paper into swirling surfaces creates sculpture that feels alive. Paper folds itself into a natural equilibrium form depending on its creases. These equilibria are poorly understood, especially for curved creases. We are exploring what shapes are possible in this genre of self-folding origami, with applications to deployable structures, manufacturing, and self-assembly. "We explore many mediums, from sculpture to performance art, video, and magic. In our artwork we look for epiphanies, challenges, and often connections and understanding to help solve problems in mathematics." --- Erik Demaine (Massachusetts Institute of Technology) http://erikdemaine.org/curved/NaturalCycles/.