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Plane polygons revisited

Published online by Cambridge University Press:  14 July 2016

B. H. Neumann
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Abstract

A method used by electrical engineers to analyse polyphase alternating current systems suggests a generalisation to arbitrary plane polygons of a theorem on triangles nowadays known, for obscure reasons, as ‘Napoleon's Theorem': the centroids of equilateral triangles erected on the sides of an arbitrary triangle form the vertices of an equilateral triangle. The generalisation to other polygons uses a construction first studied by C.-A. Laisant in 1877; results of Jesse Douglas (1940) and the author (1941) are re-derived by means of the elementary algebra of finite-dimensional vector spaces over the field of complex numbers.

Keywords

POLYPHASE ALTERNATING CURRENTPLANE POLYGONSFINITE-DIMENSIONAL VECTOR SPACES

Information

Type
Part 2 — Geometry and Geometrical Probability
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 113 - 122
Copyright
Copyright © 1982 Applied Probability Trust 

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References

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