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The tiling conjecture for equiangular polygons

Published online by Cambridge University Press:  01 August 2016

K. Robin McLean
K. Robin McLean*
Affiliation:
Dept of Education, University of Liverpool, PO Box 147, Liverpool L69 3BX
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Extract

In [1], Derek Ball made three conjectures about equiangular polygons in which the length of each side is an integer. He called these integer equiangular polygons. The first two conjectures were proved in an earlier note, and the third is proved here. It can be stated as follows.

The tiling conjecture: For each integer n ⩾ 3, there is a finite set Tn of tiles such that every integer equiangular n-gon can be tiled by sufficiently many congruent copies of tiles in Tn.

Type
Articles
Information
The Mathematical Gazette , Volume 89 , Issue 514 , March 2005 , pp. 28 - 34
Copyright
Copyright © The Mathematical Association 2005

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References

1. Ball, Derek, Equiangular polygons, Math. Gaz. 86 (November 2002) pp. 396–407.CrossRefGoogle Scholar
2. McLean, K. Robin, A powerful algebraic tool for equiangular polygons, Math. Gaz. 88 (November 2004) pp. 513–514.CrossRefGoogle Scholar
3. Stewart, I., Galois theory (1st edn), Chapman and Hall (1973).Google Scholar
4. Cohn, P.M., Algebra Volume 2 (2nd edn), John Wiley and Sons (1989).Google Scholar