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.
"Tea for Eight," by Susan Goldstine (St. Mary's College of Maryland, St. Mary's City)
Glaze on commercial ceramic, 5" x 8" x 5", 2010
The Four-Color Theorem says that we can color any map on a plane or sphere with only four colors so that no neighboring countries are the same color. On other surfaces, we may need more colors; on a two-holed torus, eight colors are sufficient, and there are maps that require all eight colors. When this tea set is stacked with the handles aligned, it forms a topological two-holed torus with a map of eight countries, each of which touches all of the others, proving that eight colors are necessary. The teapot has white, red, orange, and yellow countries, and the teacup has black, green, blue and purple countries. At the seam between the pieces, each of the top colors touches each of the bottom colors. On one-holed tori, such as the teapot and the teacup, seven colors are required for an arbitrary map. Unfortunately, a seven-color map is incompatible with the tea set's exterior pattern; when the tea set is opened, hidden colors give six-color maps of the teacup and the teapot. --- Susan Goldstine (http://faculty.smcm.edu/sgoldstine)