### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Beitrage zur Algebra und Geometrie*,

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

**On the moduli space of equilateral plane pentagons.** / Klaus, Stephan; Kojima, Sadayoshi.

Research output: Contribution to journal › Article

*Beitrage zur Algebra und Geometrie*, vol. 60, no. 3, pp. 487-497. https://doi.org/10.1007/s13366-018-0429-z

}

TY - JOUR

T1 - On the moduli space of equilateral plane pentagons

AU - Klaus, Stephan

AU - Kojima, Sadayoshi

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We give two new proofs of the well-known result that the moduli space M5 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.

AB - We give two new proofs of the well-known result that the moduli space M5 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.

KW - Closed surface

KW - Compactification

KW - Moduli space

KW - Pentagon

KW - Rational parametrization

UR - http://www.scopus.com/inward/record.url?scp=85069998723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069998723&partnerID=8YFLogxK

U2 - 10.1007/s13366-018-0429-z

DO - 10.1007/s13366-018-0429-z

M3 - Article

AN - SCOPUS:85069998723

VL - 60

SP - 487

EP - 497

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 3

ER -