Return to Gaussian curvature (idea)

Taking its name from the famous German mathematician Carl Friederich Gauss, the Gaussian curvature of a surface at a point is obtained by taking the inverse of the geometric mean (the square root of the product, in this case) of the principal curvature radii at that point.

In symbols:

G=(r*R)^(-0.5)
While other definitions of cuvature are possible and in use (e.g.: 2/(r+R), which uses the arithmetic mean) the Gaussian definition is one of the most used, as it enters several interesting properties, with developability being perhaps one of the most important.
Existing:


Non-Existing: