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.
"Frabjous," by George W. Hart (www.georgehart.com)This is an 11-inch diameter sculpture made of laser-cut wood (aspen). It is assembled from thirty identical pieces. Each is an elongated S-shaped form, with two openings. The aspen is quite light in color but the laser-cut edges are a rich contrasting brown. The openings add nicely to the whirling effect. The appearance is very different as one moves around it. This is an image of how it appears looking straight down one of the vortices. The word "frabjous" comes, of course, from "The Jabberwocky" of Lewis Carroll. "O frabjous day! Callooh! Callay!" --- George W. Hart (www.georgehart.com)
"72 Pencils," by George W. Hart (www.georgehart.com)"72 Pencils" is a geometric construction of 72 pencils, assembled into a work of art. The form is an arrangement of four intersecting hexagonal tubes that penetrate each other in a fascinating three-dimensional lattice. For some viewers, part of the interest lies in the form of the interior. The four hexagonal tubes are hollow, so the sculpture as a whole is hollow. But, what shape is its cavity? What would someone on the inside see? To the mathematician, the answer is "the rhombic dodecahedron," a geometric solid bounded by twelve rhombuses. See two other views, showing how it looks along various axes of symmetry, at www.georgehart.comwww.georgehart.com. --- George W. Hart (www.georgehart.com)