Loterre: Mathematics: Fenchel's theorem

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Fenchel's theorem

In differential geometry, Fenchel's theorem is an inequality on the total absolute curvature of a closed smooth space curve, stating that it is always at least 2π . Equivalently, the average curvature is at least ${\\displaystyle 2\\pi /L}$ , where ${\\displaystyle L}$ is the length of the curve. The only curves of this type whose total absolute curvature equals 2π and whose average curvature equals ${\\displaystyle 2\\pi /L}$ are the plane convex curves. The theorem is named after Werner Fenchel, who published it in 1929.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Fenchel%27s_theorem)

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