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.
"Bucky Madness," by Jeffrey Stewart Ely (Lewis and Clark College, Portland, OR)
Digital print on archival paper, 20" x 20", 2010
This is my response to a request to make a ball and stick model of the buckyball carbon molecule. After deciding that a strict interpretation of the molecule lacked artistic flair, I proceeded to use it as a theme. Here, the overall structure is a 60-node truncated icosahedron (buckyball), but each node is itself a buckyball. The center sphere reflects this model in its surface and also recursively reflects the whole against a mirror that is behind the observer. I was recently surprised to read in David Richeson's book, Euler's Gem, that Legendre proved Euler's Formula, V - E + F = 2, by projecting a polyhedron onto a sphere and then summing the areas of the various spherical polygons. I think this fact resonates rather well with this design. --- Jeffrey Stewart Ely