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.
"Simple Bowl (32)," by Goran Konjevod, Arizona State University, Tempe, AZ (2006)
One folded square sheet of paper, 5" x 5" x 4". "This is one of the simplest pieces in my ongoing series of bowls formed by pleat tessellations. Every fold is a straight line segment parallel to an edge of the square sheet, and no fold is ever undone. The curved surface is purely a result of the intrinsic tension in the sheet of paper trying to unfold itself. This simple bowl is constructed by using alternating pairs of vertical and horizontal pleats, from the edges toward the center." --- Goran Konjevod, Assistant Professor of Computer Science and Engineering, Arizona State University, Tempe, AZ