Napoleon polygons

Titu Andreescu, Vladimir Simeonov Gueorguiev, 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
Externally publishedYes

Fingerprint

n-gon
Polygon
Theorem
If and only if
Generalise

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Napoleon polygons. / Andreescu, Titu; Gueorguiev, Vladimir Simeonov; Mushkarov, Oleg.

In: American Mathematical Monthly, Vol. 122, No. 1, 2015, p. 24-29.

Research output: Contribution to journalArticle

Andreescu, Titu ; Gueorguiev, Vladimir Simeonov ; Mushkarov, Oleg. / Napoleon polygons. In: American Mathematical Monthly. 2015 ; Vol. 122, No. 1. pp. 24-29.
@article{af9c0c41b8cd434d89b60c2ab539ced0,
title = "Napoleon polygons",
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.",
author = "Titu Andreescu and Gueorguiev, {Vladimir Simeonov} and Oleg Mushkarov",
year = "2015",
doi = "10.4169/amer.math.monthly.122.01.24",
language = "English",
volume = "122",
pages = "24--29",
journal = "American Mathematical Monthly",
issn = "0002-9890",
publisher = "Mathematical Association of America",
number = "1",

}

TY - JOUR

T1 - Napoleon polygons

AU - Andreescu, Titu

AU - Gueorguiev, Vladimir Simeonov

AU - Mushkarov, Oleg

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84995554773&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84995554773&partnerID=8YFLogxK

U2 - 10.4169/amer.math.monthly.122.01.24

DO - 10.4169/amer.math.monthly.122.01.24

M3 - Article

VL - 122

SP - 24

EP - 29

JO - American Mathematical Monthly

JF - American Mathematical Monthly

SN - 0002-9890

IS - 1

ER -