A Short Proof of McDougall’s Circle Theorem

A Short Proof of McDougall’s Circle Theorem

This note offers a short, elementary proof of a result similar to Ptolemy’s theorem. Specifically, letdi ,jdenote the distance betweenPi andPj . Letnbe a positive integer andPi , for 1 ≤i≤ 2n, be cyclically ordered points on a circle. If then

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Bibliographic Details
Published in:The American mathematical monthly Vol. 121; no. 3; pp. 263 - 265
Main Authors: Chamberland, Marc, Zeilberger, Doron
Format: Journal Article
Language:English
Published: Washington Mathematical Association of America 01-03-2014
Taylor & Francis Ltd
Subjects:
Mathematical analysis
Proof theory
Online Access:Get full text
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Description
Summary:This note offers a short, elementary proof of a result similar to Ptolemy’s theorem. Specifically, letdi ,jdenote the distance betweenPi andPj . Letnbe a positive integer andPi , for 1 ≤i≤ 2n, be cyclically ordered points on a circle. If then
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.121.03.263