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.