Metric circle

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. 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, but this term has also been used for other concepts. 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.