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.
"Hyperbolic Tiling," by Gwen Fisher (www.beadinfinitum.com)
Materials: size 11° seed beads and thread. 63 mm diameter
This is a beaded version of the hyperbolic rhombitetrahexagonal tiling. This tiling is composed of squares and hexagons with three squares and one hexagon around every vertex. I made two of the types of squares green to emphasize the stripes in the tiling. The other type of square is purple, and the hexagons are pink. To make this tiling with bead weaving, I used an across-edge weave. In particular, for the squares, I weaved loops of four beads of the same color for each square, and loops of 6 beads for the hexagons. Then, I attached the loops with one bead per adjacent pair. So the holes of the beads that lie on the edges of the tiling are perpendicular to the the edges. --- Gwen Fisher (www.beadfinitum.com)