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.
"Icosahedron #1," by Briony Thomas (School of Design, University of Leeds, UK)
Laser-cut acrylic, 6.5" x 5.5" x 6", 2007. The successful application of a pattern to repeat across the faces of a polyhedron is determined by the pattern's underlying lattice structure and its inherent symmetry operations. Only pattern classes containing six-fold rotation are applicable to patterning icosahedron. Icosahedron #1 exhibits a p6 pattern cut from the faces of the solid. Centres of six-fold rotation in the pattern become axes of five-fold rotation at each vertex and all other rotational symmetries are preserved. "As a designer, with a background in textiles, I am fascinated by the fundamental concept of symmetry and its application in the creation of patterns. This recent work explores the possibilities of patterns repeating in three-dimensions, around the faces of mathematical solids." --- Briony Thomas (School of Design, University of Leeds, UK)