# Geodesic circle

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{{one source |date=May 2024}}
A '''geodesic circle''' is either "the [locus](/source/locus_(mathematics)) on a [surface](/source/surface_(mathematics)) at a constant [geodesic](/source/geodesic) [distance](/source/distance) from a fixed [point](/source/point_(geometry))" or a [curve](/source/curve) of constant [geodesic curvature](/source/geodesic_curvature).<ref name="Whittemore1901">{{cite journal | last=Whittemore | first=J. K. | title=A Note on Geodesic Circles | journal=The Annals of Mathematics |jstor=1967629 | volume=3 | issue=1/4 | year=1901 | pages=21–24 | issn=0003-486X | doi=10.2307/1967629 }}</ref> 
A '''geodesic disk''' is the region on a surface bounded by a geodesic circle.
In contrast with the ordinary [circle](/source/circle) and [disk](/source/disk_(mathematics)), the geodesic circle is not necessarily a [plane curve](/source/plane_curve) and the geodesic disk is not necessarily a [planar surface](/source/planar_surface).
They can be used to define ''[Gaussian curvature](/source/Gaussian_curvature)''.

==References==
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Category:Geodesic (mathematics)
Category:Circles

{{Riemannian-geometry-stub}}

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Adapted from the Wikipedia article [Geodesic circle](https://en.wikipedia.org/wiki/Geodesic_circle) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Geodesic_circle?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.