principal curvature

In mathematics, principal curvature refers to the curvatures of a surface at a specific point along two perpendicular directions. These directions are found by considering planes that contain the normal line to the surface at that point. One plane yields the maximum curvature, and the other yields the minimum curvature. These two values, the principal curvatures, are fundamental to understanding the shape of a surface. Their product gives the total or Gaussian curvature, while their average (or half their sum) is the mean curvature. This concept is part of differential geometry, which uses calculus to study curves and surfaces.12