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.
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.