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.
"Spring Forest (5,3)," by sarah-marie belcastro (Hadley, MA)
Embedded, unembedded, and cowl; 12" x 11" x 9", Knitted wool (Dream in Color Classy, in colors Happy Forest and Spring Tickle), 2009 and 2013
"I am a mathematician who knits as well as a knitter who does mathematics."
A (p,q) torus knot traverses the meridian cycle of a torus p times and the longitudinal cycle q times. Here are three instantiations of a (5,3) torus knot:
(a, middle) The knot embedded on a torus. A (p,q) torus knot may be drawn on a standard flat torus as a line of slope q/p. The challenge is to design a thickened line with constant slope on a curved surface. (b, top) The knot projection knitted with a neighborhood of the embedding torus. The knitting proceeds meridianwise, as opposed to the embedded knot, which is knitted longitudinally. Here, one must form the knitting needle into a (5,3) torus knot prior to working rounds. (c, bottom) The knot projection knitted into a cowl. The result looks like a skinny knotted torus. --- sara-marie belcastro (http://www.toroidalsnark.net)