Editing Great circle (section)

==Discussion==
Any [[Circular arc|arc]] of a great circle is a [[geodesic]] of the sphere, so that great circles in [[spherical geometry]] are the natural analog of [[Line (geometry)|straight lines]] in [[Euclidean space]]. For any pair of distinct non-[[Antipodal point|antipodal]] [[point (geometry)|point]]s on the sphere, there is a unique great circle passing through both. (Every great circle through any point also passes through its antipodal point, so there are infinitely many great circles through two antipodal points.) The shorter of the two great-circle arcs between two distinct points on the sphere is called the ''minor arc'', and is the shortest surface-path between them. Its [[arc length]] is the [[great-circle distance]] between the points (the [[intrinsic metric|intrinsic distance]] on a sphere), and is proportional to the [[angle measure|measure]] of the [[central angle]] formed by the two points and the center of the sphere.

A great circle is the largest circle that can be drawn on any given sphere. Any [[diameter]] of any great circle coincides with a diameter of the sphere, and therefore every great circle is [[Concentric objects|concentric]] with the sphere and shares the same [[radius]]. Any other [[circle of a sphere|circle of the sphere]] is called a [[small circle]], and is the intersection of the sphere with a plane not passing through its center. Small circles are the spherical-geometry analog of circles in Euclidean space.

Every circle in Euclidean 3-space is a great circle of exactly one sphere.

The [[disk (mathematics)|disk]] bounded by a great circle is called a ''great disk'': it is the intersection of a [[ball (geometry)|ball]] and a plane passing through its center.
In higher dimensions, the great circles on the [[n-sphere|''n''-sphere]] are the intersection of the ''n''-sphere with 2-planes that pass through the origin in the [[Euclidean space]] {{math|'''R'''<sup>''n'' + 1</sup>}}.

Half of a great circle may be called a ''great [[semicircle]]'' (e.g., as in parts of a [[Meridian (astronomy)|meridian in astronomy]]).