# defect

Consider a triangle $\mathrm{\u25b3}ABC$ in either hyperbolic or spherical geometry^{} (http://planetmath.org/NonEuclideanGeometry) in which its angle sum in radians is $\mathrm{\Sigma}$.

In hyperbolic geometry, the *defect* of $\mathrm{\u25b3}ABC$ is $\delta (\mathrm{\u25b3}ABC)=\pi -\mathrm{\Sigma}$.

In spherical geometry, the *defect* of $\mathrm{\u25b3}ABC$ is $\delta (\mathrm{\u25b3}ABC)=\mathrm{\Sigma}-\pi $.

Note that, in both hyperbolic and spherical geometry, the area of a is equal to its defect.

Title | defect |
---|---|

Canonical name | Defect |

Date of creation | 2013-03-22 16:05:22 |

Last modified on | 2013-03-22 16:05:22 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 10 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 51M10 |

Classification | msc 51-00 |

Related topic | AreaOfASphericalTriangle |