great circle

The intersectionMathworldPlanetmath of a sphere with a plane that passes through the center of the sphere is called a great circle. Note that it is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to say that a great circle of a sphere is any circle that lies on the surface of the sphere and has maximum circumferenceMathworldPlanetmath. 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 geometryMathworldPlanetmath, 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
Canonical name GreatCircle
Date of creation 2013-03-22 16:06:02
Last modified on 2013-03-22 16:06:02
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 10
Author Wkbj79 (1863)
Entry type Definition
Classification msc 51-00
Related topic VolumeOfSphericalCapAndSphericalSector
Defines great arc