Differential Geometry Carved in Stone
I work on geometric computation and graphics in Mathematica, and for Mathematica 6 I was responsible for our new surface-drawing capabilities. When I talk about my work at university mathematics departments, I am often told that I just have to see what the department has tucked away in some corner of its building: plaster casts of intriguing mathematical surfaces, created in the early part of the twentieth century to illustrate the achievements of the field of differential geometry.
It’s been very difficult even to reproduce those plaster casts, let alone to go beyond them—each one represents a sophisticated combination of symbolic mathematics, numerics and geometry. But with Mathematica, we now have just the combination of capabilities that are needed. And I always find it fun to reproduce those plaster-cast surfaces—often with single lines of Mathematica code, usually centered on the function ParametricPlot3D. With 3D printing, I’ve even been able to make my own physical versions of lots of these surfaces.