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.
"Rational Circles," by Stephen Schiller (Adobe Systems Inc., Oakland, CA)
Digital Print, 24” by 15.6”, 2009. This image consists of a large number of circles. To describe the set of circles let [a,b,c,d] represent the circle whose points are the zeros of the bivariate polynomial p(x,y)=a(x^2+y^2)+bx+cy+d. If a, b, and c are relatively prime integers then I call the circle a "reduced rational" circle. The drawing then consists of reduced rational circles such that a^2+b^2+c^2 <= 9^2, as viewed through a rectangle whose lower left is (0.01,0.21667) and whose upper right is (0.395,0.46667). (The view box was mostly chosen for aesthetic reasons.) The darkness of each circle depends inversely on its radius and on the term a^2+b^2+c^2. Most of my mathematical art has its origins in images I make to help me understand the solution to some problem I am facing in my work as a computer scientist. There is great power in mathematical theorems that help us understand a complex set of objects. But sometimes such theorems hide, or at least allow us to temporarily ignore, the true complexity of a subject. This duality often comes up when one tries to actually implement a mathematical idea. Thus, I find myself interested in images that are a manifestation or rediscovery of the complexity that is inherent in even simple mathematical areas." --- Stephen Schiller (Adobe Systems Inc., Oakland, CA) http://stephenschiller.imagekind.com/