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.
"Invertible Infinity," by Ellie Baker (Lexington, MA)
45 x 45 cm, silk crepe de chine (custom printed via Spoonflower.com), 2016
This reversible infinity scarf is a specially constructed cloth torus such that its shape is invariant under inversion AND it folds flat into a six-layer equilateral triangle. Since the meridians and longitudes of a torus swap places under inversion, one might think the invariance property dictates construction from a square piece of fabric (with opposite edges sewn together). However, although inversion invariance can be achieved with a square construction, the equilateral triangle folding cannot. Can you figure out a possible shape for the flat fabric layout used? The fabric designs, both P6M wallpaper group patterns that I created with Richter-Gebert’s app iOrnament, are a clue, and permitted sewing the pattern to match at the seams.The mathematical ideas incorporated into the design of this scarf were developed in collaboration with Charles Wampler. Thank you to Carol Maglitta for modeling. More information. -- Ellie Baker