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.
"Untitled, " by Jack Love (graduate student, George Mason University, Fairfax, VA)
Spherical, 18" in diameter, medium-density fiberboard, 2013
"The Platonic solids have been the inspiration for the pieces I have created thus far. My work explores the structure of these objects and their relationships to one another, and attempts to express this structure in a way that is aesthetically appealing. "
Take either the icosahedron or dodecahedron and center it at the origin. Project its vertices outward from the origin onto the surface of a sphere surrounding it, giving a collection of points on a sphere. Draw a great circle through two points if they are images of two adjacent vertices in the original polytope. Each of these great circles is partitioned into arcs by its intersection with the other great circles thus produced. The arcs come in three lengths and are projections of the edges of, respectively, an icosahedron, a dodecahedron, and a third polytope whose facets are rhombic. This model exhibits this construction. The convex arcs correspond to the icosa, the concave to the dodeca, and the straight to the rhombic. --- Jack Love