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 |
|---|---|
| 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 |