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.
"The Double-Knitting Groups," by Susan Goldstine (St. Mary's College of Maryland, St. Mary's City, MD)
40 x 40 cm, silk/merino yarn, 2016
The Double-Knitting Groups exhibits all of the wallpaper symmetry types possible in double knitting. For a harmonious overall design, I grouped the nine structures into three pattern families: scrolls, hearts, and vines. Roughly speaking, the symmetry groups get more complex from top left to bottom right: the upper left pattern has only translations, the three adjacent to it have only translations and one other type of plane symmetry (clockwise: reflections, rotations, and glide reflections), and the remaining patterns have at least three symmetry types. --- Susan Goldstine