In differential geometry, Fenchel's theorem (Werner Fenchel, 1929) states that the average curvature of any closed convex plane curve is
where P is the perimeter. More generally, for an arbitrary closed curve in space the average curvature is with equality holding only for convex plane curves.
Famous quotes containing the word theorem:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)