# biangle

In spherical geometry^{}, it is possible to form a polygon^{} with only two sides. Thus, we have the following definition:

A *biangle* is a two-sided polygon that is strictly contained in one hemisphere of the sphere that is serving as the model for spherical geometry.

Given a biangle, its vertices must be antipodal points, and its two angles must be congruent. Therefore, every biangle is equiangular. Since each side of a biangle is half of a great circle, every biangle is equilateral. Hence, every biangle is regular^{}.

Let $\theta $ be the radian measure (http://planetmath.org/AngleMeasure) of each angle of a biangle. Then the biangle covers (http://planetmath.org/Cover) $\frac{\theta}{2\pi}$ of the sphere. Since the area of the sphere is $4\pi $, the area of the biangle is $2\theta $. Note that this equals the angle sum of the biangle.

Title | biangle |
---|---|

Canonical name | Biangle |

Date of creation | 2013-03-22 17:06:10 |

Last modified on | 2013-03-22 17:06:10 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 8 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 51M10 |

Classification | msc 51-00 |