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On covering a regular polygon with a triangle

Published online by Cambridge University Press:  24 October 2008

H. G. Eggleston
Affiliation:
Bedford CollegeLondon

Extract

In this note we consider a particular type of covering problem. Let T be given a plane set and Tθ be the set obtained from T by a rotation about some point in the plane through an angle θ in the clockwise sense. If a set K is such that for every θ there is a translation which transforms Tθ into a subset of K then we say that K is a rotation cover of T. The problem considered here is to determine for fixed n, l the triangle of least area which is a rotation cover for an n-sided regular polygon of side length l. In each case the solution is an equilateral triangle the altitude of which is given by

This solution is unique.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1962

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