Gaussian Curvature
Gaussian Curvature is a measure of the intrinsic curvature of a surface at a given point. It is calculated using the product of the principal curvatures, which are the maximum and minimum curvatures of the surface in different directions. A surface can be classified as positively curved (like a sphere), negatively curved (like a saddle), or flat (like a plane) based on its Gaussian curvature.
This concept is important in differential geometry and has applications in various fields, including physics, computer graphics, and general relativity. Understanding Gaussian curvature helps in analyzing the shape and properties of surfaces in both theoretical and practical contexts.