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.
"The Susurrus of the Sea," by George W. Hart (www.georgehart.com)
Soft waves, suggestive of both sky and water, travel around the globe along six different criss-crossing equators. The susurrus (murmur) of the sea is suggested as a sense of harmony in this sphere. Technically difficult, the 60 transparent blue acrylic plastic components had to be made very precisely to fit together. Heat-formed, the components were formed and assembled on special jigs which imparted the proper dimensions and angles. Mathematically, the blue spirals are helixes that follow the edges of an icosidodecahedron. This is a polyhedron that was known to the ancient Greeks, but the oldest known drawing of it is by Leonardo da Vinci. Formally constructed of triangles and pentagons (which show up here as the openings) it can also be seen as an arrangement of six equatorial regular decagons. Each equator makes ten twists in a complete path, crossing the other five equators at two opposite points. If one "walks along" a dark blue edge, making right-angle turns where edges meet, one traces a large five-pointed star before returning to one’s starting point.