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.