# pentagon

A *pentagon ^{}* is a 5-sided planar polygon.

Regular pentagons are of particular interest for geometers. On a regular pentagon, the inner angles are equal to ${108}^{\circ}$. All ten diagonals have the same length. If $s$ is the length of a side and $d$ is the length of a diagonal, then

$$\frac{d}{s}=\frac{1+\sqrt{5}}{2};$$ |

that is, the ratio between a diagonal and a side is the Golden Number.

A regular pentagon (along with its diagonals) can also be obtained as
the projection of a regular^{} pentahedron^{} in four dimensional space
onto a plane determined by two opposite edges.
This is analogous to the way a square with its diagonals can be obtained
as the projection of a tetrahedrononto a plane determined by two opposite edges.

Title | pentagon |
---|---|

Canonical name | Pentagon |

Date of creation | 2013-03-22 12:10:19 |

Last modified on | 2013-03-22 12:10:19 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 8 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 51-00 |

Related topic | Triangle |

Related topic | Polygon^{} |

Related topic | Hexagon^{} |

Related topic | RegularDecagonInscribedInCircle |