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Napoleon Polygons

Journal article published in 2015 by Titu Andreescu, Vladimir Georgiev ORCID, Oleg Mushkarov
This paper is available in a repository.
This paper is available in a repository.

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Preprint: policy unknown
Question mark in circle
Postprint: policy unknown
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Abstract

An n-gon is called Napoleon if the centers of the regular n-gons erected outwardly on its sides are vertices of a regular n-gon. In this paper we obtain a new geometric characterization of Napoleon n-gons and give a new proof of the well-known theorem of Barlotti–Greber ([1], [4]) that an n-gon is Napoleon if and only if it is affine-regular. Moreover, we generalize this theorem by obtaining an analytic characterization of the n-gons leading to a regular n-gon after iterating the above construction k times.