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.
"A 3D model of Costa’s Minimal Surface," by O. Michael Melko (Northern State University, Aberdeen, SD)
Solid model of layered polymer resin created via stereolithography, 7 ” x 7” x 6”, 2005. Costa’s minimal surface is the first example of a complete, embedded minimal surface of finite total curvature to be discovered. This surface admits an explicit parameterization in terms of elliptic functions via the Weierstrass representation for minimal surfaces. The topology of the surface is that of a torus with three punctures, but its embedding is rather difficult to grasp visually from a typical graphical image. Hence we provide a rendering in the form of a solid model, the data for which was created with Mathematica. "As a differential geometer, I am interested in creating computer-generated forms of geometrical structures that are difficult to visualize. In addition to helping the viewer better grasp the underlying mathematics, the process of creating the work of art brings pleasure to the mathematical artist, who must be creative in his use of computational tools in order to achieve the desired outcome." --- O. Michael Melko (Northern State University, Aberdeen, SD) http://www3.northern.edu/melkom