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# great circle

The intersection of a sphere with a plane that passes through the center of the sphere is called a *great circle*. Note that it is equivalent to say that a great circle of a sphere is any circle that lies on the surface of the sphere and has maximum circumference. Geographically speaking, longitudes are examples of great circles; however, with the exception of the equator, *no* latitude is a great circle.

Infinitely many great circles pass through two antipodal points of a sphere. Otherwise, two distinct points on a sphere determine a unique great circle.

Note that great circles and great arcs are geodesics of the surface of the sphere on which they lie. Thus, in spherical geometry, if a sphere is serving as the model, then lines are defined to be great circles of the sphere, and line segments are defined to be great arcs of the sphere.

## Mathematics Subject Classification

51-00*no label found*

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