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A note on equilateral polygons

Published online by Cambridge University Press:  31 October 2008

A. D. Russell
A. D. Russell
Affiliation:
12 Heugh Street, Falkirk.
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Theorem. If a circle cut all the sides (produced if necessary) of an equilateral polygon, the algebraic sum of the intercepts between the vertices and the circle is zero; i.e., if any side AB of the polygon be cut by the circle in P and Q, then Σ(AP + BQ) = 0, the intercepts being signed by fixing a positive direction round the contour of the polygon.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 37 , January 1949 , pp. 23 - 24
Copyright
Copyright © Edinburgh Mathematical Society 1949

References

1 “Theorem regarding a regular polygon and a circle cutting its sides,” Mathematical Notes, No, 22, 1924.Google Scholar