Minimal Yet Interesting Surfaces

Some days you just run across a shape you never heard of before and that’s interesting. Matthias Weber of The Inner Frame gave me one last night. In a string of essays Weber shows a figure which comes up from minimal surface theory. This is a study of making a shape that fits to some given boundary while keeping a property called “mean curvature” equal to zero. This is how mathematicians make it sound all academic when they talk about soap bubbles in wire frames.

This is from a particular kind of surface developed in the 1860s by Alfred Enneper, whom I admit I never heard of before either. It’s just outside my specialty. But he was a student of Peter Gustav Lejeune Dirichlet, who’s just all over partial differential equations and Fourier series. Enneper and Karl Weierstrauss — whose name is all over analysis — described a way to describe these surfaces, using differential geometry. Once again I’m sad I don’t know that field more, as it produces such compelling pictures.

Here Weber introduces the surface, complete with a craft project! If you’d like you can cut out and fit together a wonderful exotic little surface. The second essay looking at some shapes with similar properties, and at what you get by stacking these surfaces. The third part extends this even farther, to the part of mathematics that’s just Googie architecture. I hope you enjoy.