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.
"Three (2k+2, 2k) links," by sarah-marie belcastro (Hadley, MA)
Knitted hand-dyed wool, 2013
A (p,q) torus link traverses the meridian cycle of a torus p times and the longitudinal cycle q times; when p and q are coprime, the result is a knot, and when not (ha!) the result is a gcd(p,q)-component link with each component a (p/gcd(p,q), p/gcd(p,q)) torus knot. Here we have (in increasing order of complexity) a (4,2) torus link, a (6,4) torus link, and an (8,6) torus link. Each is knitted so that both the knotting and the linking are intrinsic to the construction (rather than induced afterwards via grafting). They were made as proof-of-concept for the methodology for knitting torus knots and links that the artist introduced at the 2014 JMM. --- sarah-marie belcastro (http://www.toroidalsnark.net)