Mathematical Physics
The Gauss-Bonnet Theorem is a fundamental result in differential geometry that relates the geometry of a surface to its topology, specifically linking the total Gaussian curvature of a surface to its Euler characteristic. It shows that for a compact two-dimensional surface without boundary, the integral of the Gaussian curvature over the surface is equal to $2\pi$ times the Euler characteristic of the surface, providing deep insights into how curvature and shape are interconnected.
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