Gaussian curvature is one type measure of the amount of "bending" a surface undergoes at a given point which is independent of the coordinate system used to describe it.

Gaussian curvature, sometimes also called total curvature, is an intrinsic property of a space independent of the coordinate system used to describe it. The Gaussian curvature of a regular surface in R^3 at a point p is formally defined as K(p) = det(S(p)), where S is the shape operator and det denotes the determinant.

anticlastic | Brioschi formula | developable surface | elliptic point | hyperbolic point | integral curvature | mean curvature | metric tensor | minimal surface | parabolic point | planar point | scalar curvature | synclastic | total curvature | umbilic point

college level

Carl Friedrich Gauss