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.
"Geodesic Cuboctahedron 7 frequency," by Magnus Wenninger (Saint John’s Abbey, Collegeville, MN)
Papercraft, 12 inches in diameter, 2009. "Geodesic domes are well known as architectural structures, but generally they exhibit only triangular grids. My main interest, however, has been in having geometric patterns projected onto a spherical surface. The icosahedron is most frequently used for this purpose, but other polyhedrons can serve just as well for the same purpose. 'Geodesic Cuboctahedron 7 frequency' is the cuboctahedron in a 7 frequency basket weave pattern with 6 squares of one color and 12 rectangles of 6 other colors projected onto the surface of the cuboctahedron’s circumsphere." More information about the techniques I use to produce my artistic patterns on a spherical surface can be found in the Dover publication of my book Spherical Models (1999), originally the Cambridge University Press publication of Spherical Models (1979). Robert Webb’s Stella program is now my computer program par excellence. --- Magnus Wenninger (Saint John’s Abbey, Collegeville, MN) http://www.saintjohnsabbey.org/wenninger/