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.
"Hyperbolic Constellation," by Susan Goldstine (St. Mary's College of Maryland, St. Mary's City, MD)
Glass beads, crochet cotton thread, 2014
Hyperbolic Constellation is inspired by Daina Taimina's innovative technique for crocheting hyperbolic surfaces. Her breakthrough is that if you crochet with an increase (made by stitching twice into the same stitch) every n stitches for a fixed number n, the result has constant negative curvature. I have always been curious about how these increases are arranged. While many artists have woven hyperbolic surfaces with beads, I have yet to see other examples of hyperbolic bead crochet, which moves more organically. In this pseudospherical beaded surface, the gold beads (every 6th bead on the thread) mark the locations of the crochet increases. The initial round contains 6 beads, while the outer edge contains 6 x 64 = 384 beads. --- Susan Goldstine (http://faculty.smcm.edu/sgoldstine)