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.
"Window into Infinity: A Sample of the Murhombicuboctahedron," by S. Louise Gould (Central Connecticut State University, New Britain)
6.5" x 6.5" x 6.5", Embroidery on cotton fabric, 2012
This is an extension of the work I have done with fabric polyhedra. "The Symmetries of Things" written by Conway, Burgiel and Goodman-Strauss has provided many pathways to explore and it was the inspiration for this piece. This Archimedean infinite polyhedra is constructed of regular hexagons and squares. It illustrates the symmetry *642. Each vertex has 4 squares and one hexagon surrounding it. This model uses squares of four colors to show how the model moves into space. Each of the modules is constructed from a "net" of embroidered squares and hexagons. The nets were designed on Geometer's Sketchpad then digitized using 4-D Professional Software and stitched on a Viking Topaz embroidery sewing machine. The pictures show the object from three different directions. -- S. Louise Gould