Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-14T07:52:59.800Z Has data issue: false hasContentIssue false

Napoleon triangles and adventitious angles

Published online by Cambridge University Press:  01 August 2016

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

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
Copyright
Copyright © The Mathematical Association 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited, Mathematical Association of America (1967).Google Scholar
2. Johnson, R. A., Advanced Euclidean geometry, Dover Publications (1960).Google Scholar
3. Schumann, H. and Green, D., Discovering geometry with a computer, Chartwell-Bratt (1994).Google Scholar
4. Barabara, Roy, A corollary of Napoleon’s Theorem, Math. Gaz. 82 (July 1998) pp. 297298.Google Scholar
5. Wells, D., The Penguin dictionary of curious and interesting geometry, Penguin (1991).Google Scholar