A geodesic circle is either "the locus on a surface at a constant geodesic distance from a fixed point" or a curve of constant geodesic curvature.1 A geodesic disk is the region on a surface bounded by a geodesic circle. In contrast with the ordinary circle and disk, the geodesic circle is not necessarily a plane curve and the geodesic disk is not necessarily a planar surface. They can be used to define Gaussian curvature.
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Last revised May 31, 2026
Geodesic circle
A geodesic circle is either "the locus on a surface at a constant geodesic distance from a fixed point" or a curve of constant geodesic curvature. A geodesic disk is the region on a surface bounded by a geodesic circle. In contrast with the ordinary circle and disk, the geodesic circle is not necessarily a plane curve and the geodesic disk is not necessarily a planar surface. They can be used to define Gaussian curvature.