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.
"Puzzle Pieces from a Sierra Sunset," by Frank A. Farris, Santa Clara University, CA. Courtesy of Princeton University Press
Digital print on aluminum, 20" x 16", 2012
Photographs with rather minimal variation (and artistic value) can turn into beautiful patterns. Can you find the color-reversing symmetry? If you turn the pink puzzle pieces 90°, they match the green ones with the same shapes but opposite colors. The inset at the lower right shows that my source photograph is actually a collage, combining the original sunset photo with its negative, rotated upside down. Again, the black band is considered a neutral color to separate positive and negative colors. --- Frank A. Farris