# ideal triangle

In hyperbolic geometry, an *ideal triangle* is a set of three lines which connect three distinct points on the boundary of the model of hyperbolic geometry.

Below is an example of an ideal triangle in the Beltrami-Klein model:

Below is an example of an ideal triangle in the Poincaré disc model:

Below are some examples of ideal triangles in the upper half plane model:

speaking, none of these figures are triangles in hyperbolic geometry; however, ideal triangles are useful for proving that, given $r\in \mathbb{R}$ with $$, there is a triangle in hyperbolic geometry whose angle sum in radians is equal to $r$.

Title | ideal triangle |
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Canonical name | IdealTriangle |

Date of creation | 2013-03-22 17:08:26 |

Last modified on | 2013-03-22 17:08:26 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 5 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 51M10 |

Classification | msc 51-00 |

Related topic | LimitingTriangle |