### Abstract

The vertices of a convex planar nonagon determine exactly five distances if and only if they are nine vertices of a regular 10-gon or a regular 11-gon. This result has important ties to related concerns, including the maximum number of points in the plane that determine exactly five distances and, for each n ≥ 7, the smallest t for which there exists a convex n-gon whose vertices determine t distances and are not all on one circle.

Original language | English |
---|---|

Pages (from-to) | 317-332 |

Number of pages | 16 |

Journal | Geometriae Dedicata |

Volume | 60 |

Issue number | 3 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Convex nonagons
- Erdös conjecture
- Intervertex distances
- Lattice theory

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Geometriae Dedicata*,

*60*(3), 317-332.

**Convex nonagons with five intervertex distances.** / Erdős, P.; Fishburn, Peter.

Research output: Contribution to journal › Article

*Geometriae Dedicata*, vol. 60, no. 3, pp. 317-332.

}

TY - JOUR

T1 - Convex nonagons with five intervertex distances

AU - Erdős, P.

AU - Fishburn, Peter

PY - 1996

Y1 - 1996

N2 - The vertices of a convex planar nonagon determine exactly five distances if and only if they are nine vertices of a regular 10-gon or a regular 11-gon. This result has important ties to related concerns, including the maximum number of points in the plane that determine exactly five distances and, for each n ≥ 7, the smallest t for which there exists a convex n-gon whose vertices determine t distances and are not all on one circle.

AB - The vertices of a convex planar nonagon determine exactly five distances if and only if they are nine vertices of a regular 10-gon or a regular 11-gon. This result has important ties to related concerns, including the maximum number of points in the plane that determine exactly five distances and, for each n ≥ 7, the smallest t for which there exists a convex n-gon whose vertices determine t distances and are not all on one circle.

KW - Convex nonagons

KW - Erdös conjecture

KW - Intervertex distances

KW - Lattice theory

UR - http://www.scopus.com/inward/record.url?scp=0041739720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041739720&partnerID=8YFLogxK

M3 - Article

VL - 60

SP - 317

EP - 332

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 3

ER -