Abstract
A.S. Besicovitch [1] and L. W. Danzer [3] characterized the circle among closed convex curves in the plane by the so-called rectangle property (for a precise definition see below). T. Zamfirescu [10] introduced an infinitesimal version of this property and proved, that a closed Jordan curve in the plane satisfying the infinitesimal rectangle property must be a convex curve of constant width. This generalizes the BesicovitchDanzer Theorem to closed Jordan curves.
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