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.
"K_7 embedded on a torus," by sarah-marie belcastro (Hadley, MA)
11" x 11" x 4.5", Knitted cotton (Reynolds Saucy), 2010
I am a mathematician who knits as well as a knitter who does mathematics. It has always seemed natural to me to combine mathematics and knitting, and it is inevitable that sometimes the results will be artistic rather than functional. The Heawood bound shows that K_7 is the largest complete graph that can embed on the torus. This is an embedding of K_7 on the torus with all vertices centered on the largest longitude. It is the second knitted instantiation of this embedding; this version is larger and has a larger face-to-edge proportion than the first, which was exhibited at Gathering for Gardner 7 in 2006. --- sarah-marie belcastro (Hadley, MA, http://www.toroidalsnark.net)