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.
"Borromean links cage," by Roger Bagula (Lakeside, CA)
3.4" x 3.2" x 0.9", White plastic, 2012
The art work is made using Mathematica and 3d models that can be printed are obtained for most of the work. Since I was a boy I have drawn jet air planes and I have made a number of 3d models what I imagined. I have been studying ruled surfaces determined by torus knots and Möbius connecting surfaces. Here three links in a Borromean configuration are bridged by a cage surface. The bridge surface is not a Seifert surface, but a simple set of ruled Bezier surfaces. --- Roger Bagula