Gaussian curvature is a measure of the intrinsic curvature of a surface at a point, defined as the product of the principal curvatures at that point. This concept helps to classify surfaces as elliptic, parabolic, or hyperbolic based on the values of these curvatures. Understanding Gaussian curvature is crucial when analyzing the geometric properties of parametrized surfaces, as it provides insight into how the surface bends in different directions.
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