Affinely regular polygons in an affine plane

Gábor Korchmáros, Tamás Szőnyi


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.

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Contributions to Discrete Mathematics. ISSN: 1715-0868