Gauss-Bonnet theorem for surfaces without boundary

If $S$ is a compact, orientable surface without boundary, then

\\int_{S}K=2\\pi\\,\\chi(S),

where $K$ is the Gaussian curvature of $S$ and $\\chi(S)$ itsEuler-Poincaré characteristic. (http://planetmath.org/EulerrCharacteristic)

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