Spherical circle

Mathematical expression of circle like slices of sphere

In spherical geometry, a spherical circle is the locus of points on a sphere at constant spherical distance from a given point on the sphere. It is a curve of constant geodesic curvature relative to the sphere, analogous to a line or circle in the Euclidean plane; the curves analogous to straight lines are called great circles, and the curves analogous to planar circles are called small circles or lesser circles. If the sphere is embedded in three-dimensional Euclidean space, its circles are the intersections of the sphere with planes, and the great circles are intersections with planes passing through the center of the sphere.

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