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.
"45 Poppies," by Karl Kattchee (University of Wisconsin-La Crosse)
Digital print, 18 x 31 cm, 2015
Best photograph, painting, or print, 2016 Mathematical Art Exhibition
This image is a classification of all closed paths, on a 6x6 grid, with the following properties: First, each path must proceed around the center of the grid and be orthogonal in the sense that every turn is 90 degrees. Also, the path must use each row and column exactly once. Finally, we require that each path be asymmetrical, and we do not distinguish between paths which differ by a rotation or flip. Each center square is colored black, and the shades of red are dictated by the winding number of each region. Acknowledgements: Craig Kaplan (Waterloo), for helpful notation and the coloring scheme idea, and artists Kate Hawkes and Misha Bolstad (UW-La Crosse) for the poppies idea. --- Karl Kattchee