In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ1 and κ2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way it is isometrically embedded in space. This result is the content of Gauss's Theorema egregium.
Symbolically, the Gaussian curvature Κ is defined as
- .
where κ1 and κ2 are the principal curvatures.
Read more about Gaussian Curvature: Informal Definition, Further Informal Discussion, Alternative Definitions, Total Curvature, Surfaces of Constant Curvature, Alternative Formulas