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.
"Octahedral Cluster," by Gwen Fisher (www.beadinfinitum.com) Copyright 2005 by Gwen L. Fisher.
Materials: white opalite glass, seed beads, Nymo nylon thread
The regular octahedron has 8 triangular faces, 6 vertices each of valence 4, and 12 edges. These 12 edges correspond to the 12 largest (white) beads in the Octahedral Cluster beaded bead. The 6 vertices of the octahedron appear as 6 stars with 4 points each. The 8 triangular faces correspond to where the points of the stars meet. This beaded bead is hollow, yet structurally stable. The stability comes from the way the small beads fit snugly into the spaces between the larger beads. The beaded bead shows virtually no thread; only beads are visible. It is springy between the fingertips and reforms its shape remarkably well. When free from compression, it is round from every angle. -- Gwen Fisher (www.beadinfinitum.com)