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.
"Blue Ionic Polyhedra: 12 Beaded Beads in Two Sizes," by Gwen Fisher (bead Infinitum, Sunnyvale, CA)
Bead weaving with crystal, glass and metal beads, and thread, 12 beads, longest diameter ranges from 11 mm to 33 mm, 2010
The Ionic Polyhedra are part of my larger body of mathematical artwork in beaded beads. A beaded bead is a cluster of smaller beads, woven together with a needle and thread, to form a composite cluster with one or more holes running though the center of the finished beaded bead. To make these beads, I started with inner cluster of beads in two sizes where the larger beads are aligned on the edges of polyhedra. For the larger six beads, I added layers of seed beads, which emphasize the edges of the underlying polyhedra. Although they appear different, the miniature version of each Ionic Polyhedron maintains the same structure and thread path as its larger version, but the beads are smaller, and the embellishment is simpler. Represented are the octahedron, cube, pentagonal dipyramid, pentagonal antiprism, cuboctahedron, and rhombic dodecahedron. This coloring of the miniature cuboctahedron and rhombic dodecahedron illustrates the dual relationship between these two polyhedra. --- Gwen Fisher (http://www.beadinfinitum.com)