### 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 language | English |
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Pages (from-to) | 24-29 |

Number of pages | 6 |

Journal | American Mathematical Monthly |

Volume | 122 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Andreescu, T., Georgiev, V., & Mushkarov, O. (2015). Napoleon polygons.

*American Mathematical Monthly*,*122*(1), 24-29. https://doi.org/10.4169/amer.math.monthly.122.01.24