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What is the most symmetric quadrilateral?

Published online by Cambridge University Press:  23 January 2015

A. F. Beardon
A. F. Beardon*
Affiliation:
Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, e-mail: ajb@dpmms.cam.ac.uk
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Extract

What is the most symmetric quadrilateral you can think of? Most people would say ‘a square’, but having given this (or any other) answer, can you create your own definition of a ‘quadrilateral’, and of ‘most symmetric’, so that you can justify your answer as a rigorous piece of mathematics? This is a challenging investigation because the answer may not be the obvious one.

Often the main difficulty in solving a problem lies in finding appropriate definitions; here we must first consider the questions ‘what is a quadrilateral?’, and ‘what is a symmetry of a quadrilateral?’.

Type
Articles
Information
The Mathematical Gazette , Volume 96 , Issue 536 , July 2012 , pp. 207 - 212
Copyright
Copyright © The Mathematical Association 2012

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References

1. Ledermann, W., Introduction to group theory, Oliver & Boyd (1973).Google Scholar
2. Budden, F. J., The fascination of groups, Cambridge University Press (1972).Google Scholar