### Abstract

We give two new proofs of the well-known result that the moduli space M_{5} of equilateral plane pentagons is a closed surface of genus four. Moreover, we construct a new algebraic description of this space, also in the non-equilateral case, as a real affine algebraic surface F defined by a polynomial p(x, y, z) of degree 12. This allows a visualization using the Surfer software.

Original language | English |
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Pages (from-to) | 487-497 |

Number of pages | 11 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 60 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2019 Sep 1 |

### Keywords

- Closed surface
- Compactification
- Moduli space
- Pentagon
- Rational parametrization

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Klaus, S., & Kojima, S. (2019). On the moduli space of equilateral plane pentagons.

*Beitrage zur Algebra und Geometrie*,*60*(3), 487-497. https://doi.org/10.1007/s13366-018-0429-z