Fenchel's theorem

Fenchel's theorem This article is about the concept in geometry. For the concept in mathematical optimization, see Fenchel's duality theorem. Fenchel's theorem Type Theorem Field Differential geometry Statement A circle with radius r has average curvature 1/r=2π/P, where P=2πr is the perimeter. Conjectured by Werner Fenchel Conjectured in 1929 En géométrie différentielle, Fenchel's theorem states that the average curvature of any closed convex curve in the Euclidean plane equals {displaystyle 2pi /L} , où {displaystyle L} is the length of the curve. It is named after Werner Fenchel, qui l'a publié dans 1929. Plus généralement, for an arbitrary closed space curve the average curvature is {displaystyle geq 2pi /L} with equality holding only for convex plane curves.

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