# 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.

An arc of a great circle is called a great arc.

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 are defined to be great circles of the sphere, and are defined to be great arcs of the sphere.

Title great circle GreatCircle 2013-03-22 16:06:02 2013-03-22 16:06:02 Wkbj79 (1863) Wkbj79 (1863) 10 Wkbj79 (1863) Definition msc 51-00 VolumeOfSphericalCapAndSphericalSector great arc