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.
"Beaded Super Right Angle Weave Quilt for a Group of Order 18 (detail)," by Gwen Fisher (www.beadinfinitum.com)
Materials: seed beads in sizes 8°, 11°, 15°, thread, silk and cotton fabric, and batting. 13 inches square.
This piece began as a study in color for what I call Super Right Angle Weave (SRAW), a bead weave based upon the regular tiling by squares. Each beaded patch is 6 square by 6 squares of the tiling. I weave loops of four beads in each square face and attach these loops across the edges of the tiling with a single bead between the loops. For this set, I use a coloring with three bead types (two types for the faces and one type for the edges). I chose three colors in each of three sizes, for a total of nine different bead types. The 18 patches are arranged in sets of three, where each row uses the same three bead types, but arranged differently. The patches of beadwork correspond to a group of order 18, and Tom Davis identified this group as the generalized dihedral group for E9. --- Gwen Fisher (www.beadfinitum.com)