Napoleon polygons

Titu Andreescu, Vladimir Georgiev, Oleg Mushkarov

研究成果: Article

2 引用 (Scopus)

抜粋

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.

元の言語English
ページ(範囲)24-29
ページ数6
ジャーナルAmerican Mathematical Monthly
122
発行部数1
DOI
出版物ステータスPublished - 2015 1 1
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)

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