Napoleon revisited
type: Item
instance of: scholarly article
title: Napoleon revisited
zbMATH Open document ID: 0655.52003
DOI: 10.1007/BF01230612
published in: Journal of Geometry
publication date: 1988-01-01T00:00:00Z
review text: A classical result (``Napoleon's theorem'') says that if equilateral triangles are erected externally or internally on the side of any triangle in the plane, then their centres form an equilateral triangle. In the present paper, several generalizations of this result are proved; for example, the following is proved: if three similar triangles PCB, CQA, BAR are erected on the sides of any triangle ABC, and if U, V, W are corresponding points of the three triangles, then UVW is similar to the three triangles. By reproducing the triangles we can obtain a tessellation of the plane: properties of these tessellations (and lattice properties of the centres of the triangles) are then considered.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 51M05
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 4069703
zbMATH Keywords: Napoleon's theorem
zbMATH Keywords: triangles
zbMATH Keywords: tessellation of the plane
author: John F. Rigby
reviewed by: Pier Luigi Papini
MaRDI profile type: Publication
Wikidata QID: Q29540587
cites work: Q3254794
cites work: Q5573028
cites work: Q5550848
cites work: Some Remarks on Polygons†
full work available at URL: https://doi.org/10.1007/bf01230612
OpenAlex ID: W4229894990
description: scientific article; zbMATH DE number 4069703