Napoleon polygons

Titu Andreescu, Vladimir Georgiev, Oleg Mushkarov

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)24-29
Number of pages6
JournalAmerican Mathematical Monthly
Volume122
Issue number1
DOIs
Publication statusPublished - 2015 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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