Gaussian curvature
Gaussian curvature is a measure of how a surface bends in different directions. Imagine the surface of a balloon: when fully inflated, it's curved in all directions and has positive curvature. A flat sheet of paper has zero curvature, while a saddle shape curves up in one direction and down in another, indicating negative curvature. Gaussian curvature combines these curvatures into a single value. It helps characterize surfaces in geometry and has applications in understanding shapes in physics, architecture, and even in modeling the universe in general relativity.
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Gaussian curvature is a measure of how a surface bends in space. It combines the curvature of the surface in two perpendicular directions. Positive Gaussian curvature means a surface curves like a sphere (bulging out), negative curvature means it curves like a saddle (dipping in one direction while bulging in another), and zero curvature describes a flat surface, like a plane. Essentially, Gaussian curvature helps us understand the shape and geometry of surfaces, revealing how they can stretch, bend, or twist in three-dimensional space.