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.
"Walking the Water's Edge," by Diane Herrmann (University of Chicago, IL)
Needlepoint on canvas, 14" x 14", 2009
In this piece, the line imitates the edge of a wave on the shore. To make this wave look realistic, we used a mathematical curve that models the way a wave breaks on the beach. To be mathematically precise, we work with the sum of two trigonometric curves to show the action of water as it sloshes over itself in the push to get on the shore. The graph that defines the line of the Florentine Stitches is a close approximation to the curve: f (x) = 5 sin x + 4 cos (2x + π/3). The technique of thread blending creates the shading of the wave. Freeform eyelet stitches mimic the foamy edge of the wave and beads add sparkle. A single starfish is added in Bullion Knots. --- Diane Herrmann