High Quality Content by WIKIPEDIA articles! In Riemannian geometry, the filling radius of a Riemannian manifold X is a metric invariant of X. It was originally introduced in 1983 by Mikhail Gromov, who used it to prove his systolic inequality for essential manifolds, vastly generalizing Loewner's torus inequality and Pu's inequality for the real projective plane, and creating Systolic geometry in its modern form.The filling radius of the Riemannian circle of length 2?, i.e. the unit circle with the induced Riemannian distance function, equals ?/3, i.e. a sixth of its length.

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