Editing Spherical circle (section)

=== Intrinsic characterization ===

A spherical circle with zero geodesic curvature is called a ''great circle'', and is a [[geodesic]] analogous to a straight line in the plane. A great circle separates the sphere into two equal ''[[Hemisphere (geometry)|hemispheres]]'', each with the great circle as its boundary. If a great circle passes through a point on the sphere, it also passes through the [[antipodal point]] (the unique furthest other point on the sphere). For any pair of distinct non-antipodal points, a unique great circle passes through both. Any two points on a great circle separate it into two ''arcs'' analogous to [[line segment]]s in the plane; the shorter is called the ''minor arc'' and is the shortest path between the points, and the longer is called the ''major arc''.

A circle with non-zero geodesic curvature is called a ''small circle'', and is analogous to a circle in the plane. A small circle separates the sphere into two ''spherical disks'' or ''[[spherical cap]]s'', each with the circle as its boundary. For any triple of distinct non-antipodal points a unique small circle passes through all three. Any two points on the small circle separate it into two ''arcs'', analogous to [[circular arc]]s in the plane.

Every circle has two antipodal poles (or centers) intrinsic to the sphere. A great circle is equidistant to its poles, while a small circle is closer to one pole than the other. [[Concentric]] circles are sometimes called ''parallels'', because they each have constant distance to each-other, and in particular to their concentric great circle, and are in that sense analogous to [[parallel line]]s in the plane.