A characterization of affinely regular polygons

A characterization of affinely regular polygons

We characterize affinely regular polygons in a real affine space as follows. Consider two polygons P and Q with the same number of vertices and a common side, P being an affine image of some (convex or nonconvex) regular polygon. Q is then an affine image of the same regular polygon if and only if t...

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Veröffentlicht in:Beiträge zur Algebra und Geometrie 2016-06, Vol.57 (2), p.453-458
1. Verfasser: Nicollier, Grégoire
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung:We characterize affinely regular polygons in a real affine space as follows. Consider two polygons P and Q with the same number of vertices and a common side, P being an affine image of some (convex or nonconvex) regular polygon. Q is then an affine image of the same regular polygon if and only if the vectors between the corresponding vertices of P and Q are uniquely determined multiples of the vector between the vertices just after the common side.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-015-0271-5