Steve Trettel

MediumMathematica Notebook
The ArtAn approximation to a Willmore torus, embedded in the 3-sphere. The surface is viewed perspectively correct from a position in 4-dimensional space off of the surface of the sphere, as the sphere rotates below it.
The MathThe Willmore energy of an embedded surface is the integral of the square of its mean curvature. A Willmore torus is an embedding of the torus (here into the 3-sphere) which is a critical point of this functional. Infinitely many of these exist, and one method of production (due to Ulrich Pinkall) involves considering the preimage of certain curves on the 2-sphere under the Hopf map.
CategoriesMathematical Illustration, Surfaces, Low Dimensional Topology, Geometric Topology