### Abstract

In this paper we survey results about affinely regular polygons. First, the definitions and classification of affinely regular polygons are given. Then the theory of Bachmann-Schmidt is outlined. There are several classical theorems about regular polygons, some of them having analogues in finite planes, such as the Napoleon-Barlotti theorem. Such analogues, variants of classical theorems are also collected. Affinely regular polygons occur in many combinatorial problems for sets in a finite plane. Some of these results about sharply focused arcs, internal and external nuclei, complete arcs are collected. Finally, bounds on the number of chords of an affinely regular polygon through a point are discussed.

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

Pages (from-to) | 20-38 |

Number of pages | 19 |

Journal | Contributions to Discrete Mathematics |

Volume | 3 |

Issue number | 1 |

Publication status | Published - Jan 1 2008 |

### Keywords

- Affinely regular polygon
- Internal and external nucleus
- Sharply focused arc

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'Affinely regular polygons in an affine plane'. Together they form a unique fingerprint.

## Cite this

*Contributions to Discrete Mathematics*,

*3*(1), 20-38.