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.
"Longest Crease/Perfect Shuffle-1," by Sharol Nau (Northfield, MN)
Folded Book, 2014
A classical calculus problem, the so-called Paper Creasing Problem is essential to the design of these sculptures. Pages in a book provide a series of rectangular sheets of paper which are creased by matching one corner; say the lower right-hand corner to a point on the opposite edge where the sheets have been bound. Waves are obtained through incremental changes in the length of the crease from page to page. Two sets of points have been used for these new examples. In each case every other page begins its sequence at a different point. The result of the two series interleaved is a so-called perfect shuffle. --- Sharol Nau (http://www.sharolnau.com)