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.
"Cuboctahedral Symmetries to Travel," by S. Louise Gould (Connecticut State University, New Britain)
Original digitized machine stitched patterns on cotton reinforced by Timtex, Five moveable pieces, collapsible each 3” × 3” ×3”, 2009. Conway enumerates the 7 spherical symmetries compatible with the uniform polyhedra in “The Symmetries of Things.” Using the symmetry types these are 332, *332, 432, 3*2, *432, 532 and *532. The simple cuboctahedron exhibits the first 5 of the symmetry patterns: *432 has 48 symmetries (the full group of symmetries), *332, 432 and 3*2 have 24 (the three subgroups of index 2=48/24) while 332 has only 12 (the ones of index 4=48/12). Coloring the faces of the models for the Archimedean solids is a natural extension of my recent work with pop-up polyhedra. "My mathematical art grows out of my experiences with my students and my explorations of mathematics, textiles, paper, and technology. I enjoy working with computer controlled machines such as the computerized embroidery sewing machine and the Craft Robo (plotter cutter) as well as traditional looms and knitting machines." --- S. Louise Gould (Connecticut State University, New Britain)