# 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 |