Metric circle
Great circle with a characteristic length / From Wikipedia, the free encyclopedia
In mathematics, a metric circle is the metric space of arc length on a circle, or equivalently on any rectifiable simple closed curve of bounded length.[1] The metric spaces that can be embedded into metric circles can be characterized by a four-point triangle equality.
Some authors have called metric circles Riemannian circles, especially in connection with the filling area conjecture in Riemannian geometry,[2] but this term has also been used for other concepts.[3] A metric circle, defined in this way, is unrelated to and should be distinguished from a metric ball, the subset of a metric space within a given radius from a central point.