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.
Hopf Knott is the offspring of two forms that have intrigued me for some time, the Hopf Link and the Borromean Rings. While the sculpture may appear to be a series of connected Hopf Links, it is actually two sets of Borromean Rings, an inner set and an outer set. Of course, the "rings" are stretched to make the crossings possible and shaped to resemble Hopf Links. The 6 outermost points correspond to the vertices of a regular octahedron. --- Peter Sittner