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
Famous quotes containing the word circle:
“Everything here below beneath the sun is subject to continual change; and perhaps there is nothing which can be called more inconstant than opinion, which turns round in an everlasting circle like the wheel of fortune. He who reaps praise today is overwhelmed with biting censure tomorrow; today we trample under foot the man who tomorrow will be raised far above us.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)