Editing Spherical circle (section)

{{short description|Mathematical expression of circle like slices of sphere}}
{{Redirect|Small circle|the typographical symbol|Degree symbol}}
{{inline |date=May 2024}}
[[Image:Small circle.svg|right|thumb|Small circle of a sphere.]]
In [[spherical geometry]], a '''spherical circle''' (often shortened to '''circle''') is the [[locus (mathematics)|locus]] of [[point (geometry)|point]]s on a [[sphere]] at constant [[great-circle distance|spherical distance]] (the ''spherical radius'') from a given point on the sphere (the ''pole'' or ''spherical center'').  It is a [[curve]] of constant [[geodesic curvature]] relative to the sphere, analogous to a [[Generalised circle|line or circle]] in the [[Euclidean plane]]; the curves analogous to [[straight lines]] are called ''[[great circle]]s'', and the curves analogous to planar [[circle]]s are called '''small circles''' or '''lesser circles'''. If the sphere is embedded in three-dimensional [[Euclidean space]], its circles are the [[intersection (geometry)|intersections]] of the sphere with [[plane (geometry)|planes]], and the great circles are intersections with planes passing through the [[center (geometry)|center]] of the sphere.