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Napoleon triangles and adventitious angles

Published online by Cambridge University Press:  01 August 2016

Michael Fox
Michael Fox*
Affiliation:
2 Learn Road, Leamington Spa, Warwickshire CV31 3PA
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Extract

In this article I investigate Napoleon triangles, generalisations of the mysterious equilateral triangle in Napoleon’s theorem. I start with that theorem, develop some analogous results, find configurations with unexpected integer angles, and return to an extension of Napoleon’s theorem. Many of the geometrical proofs depend upon spiral similarities, and the numerical work uses some unfamiliar trigonometrical identities.

Type
Articles
Information
The Mathematical Gazette , Volume 82 , Issue 495 , November 1998 , pp. 413 - 422
Copyright
Copyright © The Mathematical Association 1998

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References

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