Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 433-444 (2002)

Napoleon's Theorem and Generalizations Through Linear Maps

Hellmuth Stachel

Institute of Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-10/113, A-1040 Wien, Austria, e-mail: stachel@geometrie.tuwien.ac.at

Abstract: Recently J. Fukuta and Z. Cerin showed how regular hexagons can be associated to any triangle, thus extending Napoleon's theorem. The aim of this paper is to prove that these results are closely related to linear maps. This reflects better the affine character of some constructions and gives also rise to a few new theorems.

Keywords: Napoleon's theorem, triangle, regular hexagon, linear map

Classification (MSC2000): 51M04

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