In metric space theory and Riemannian geometry, the **Riemannian circle** (named after Bernhard Riemann) is a great circle equipped with its great-circle distance. In more detail, the term refers to the circle equipped with its *intrinsic* Riemannian metric of a compact 1-dimensional manifold of total length 2π, as opposed to the *extrinsic* metric obtained by restriction of the Euclidean metric to the unit circle in the plane. Thus, the distance between a pair of points is defined to be the length of the shorter of the two arcs into which the circle is partitioned by the two points.

Read more about Riemannian Circle: Properties, Gromov's Filling Conjecture

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### Famous quotes containing the word circle:

“They will mark the stone-battlements

And the *circle* of them

With a bright stain.

They will cast out the dead

A sight for Priam’s queen to lament

And her frightened daughters.”

—Hilda Doolittle (1886–1961)