Gaussian curvature is a numerical quantity associated with an area of a surface that describes the intrinsic geometric property of that area. It is different from the curvature of a curve, for that is an extrinsic geometric property defining how it is bent in a plane or space. The Gaussian curvature remains the same no matter how a surface is bent as long as it is not distorted. It is defined as the product of the principal curvatures, the maximum and minimum values of normal curvature at a point on a surface. Since it is the product of two curvatures, Gaussian curvature has the units of curvature squared. If the Gaussian curvature is a positive value then the surface is locally either a peak (both the maximum and minimum values are positive, hence the product is positive) or a valley (both the maximum and minimum values...