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.
"Tetra-Tangle of Four Bow-Tie Links," by Carlo Séquin (University of California, Berkeley)
ABS plastic, printed on an FDM machine, 2014
Four sets of three mutually parallel, 3-sided prisms, pointing in 4 different tetrahedral directions, form the core of the TETRAXIS® puzzle. When two triangular prism-end-faces that share a common vertex are closed off with a connecting sweep, a loose "bow-tie" is formed. If all twelve pairs of adjoining triangular end-faces are joined in this manner, the result is a link of 4 mutually interlocking, twisted, prismatic bow-tie loops. This represents an alternating 12-crossing link that has the same connectivity as the “Tetra-Tangle,” which I constructed from 4”-diameter card-board tubes in 1983. The new geometry is has been realized as 4 differently colored sets of 6 tubular snap-together parts each, fabricated on an FDM machine. --- Carlo Séquin (http://www.cs.berkeley.edu/~sequin/)