The Differential Geometry of the Sphericon


6. The total curvature of the Sphericon

According to the Gauss-Bonnet Theorem, the total curvature of a smooth convex surface is 4. We can check that this statement holds for the more exotic curvature of the Sphericon.

The Sphericon has four cone-points and two arcs of zip-loci. Otherwise it has no curvature, since it can be assembled from flat pieces without stretching.

On to Sphericon page 7.

Back to Sphericon page 5.

© copyright 1999, American Mathematical Society.