"A 3D model of Costa’s Minimal Surface"

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.

O. Michael Melko, Assistant Professor of Mathematics, Department of Mathematics
Northern State University, Aberdeen, South Dakota

"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."