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Octagrammum mysticum and the golden cross-ratio

Published online by Cambridge University Press:  01 August 2016

Lawrence S. Evans  and
John F. Rigby
Lawrence S. Evans
Affiliation:
910 West 57th Street, La Grange IL 60525, USA email: 75342.3052@compuserve.com
John F. Rigby
Affiliation:
School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH email: rigby@cardiff.ac.uk
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Extract

When the authors met at a geometry conference at Easter 1999, they found that each had discovered and investigated an elegant result (Theorem 2.1) about an octagon inscribed in a conic, Larry Evans algebraically and John Rigby synmetically. This turned out to be a rediscovery, as the result had been discussed by E. H. Lockwood in the Gazette in 1967, in an article that complements the present article. Also, almost a century earlier in 1872, the result had been posed somewhat imprecisely by T. T. Wilkinson as a problem in the Educational Times. There is a surprising connection between a special case of the octagon theorem and the golden cross-ratio.

Type
Articles
Information
The Mathematical Gazette , Volume 86 , Issue 505 , March 2002 , pp. 35 - 43
Copyright
Copyright © The Mathematical Association 2002

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References

1. Lockwood, E. H. An octagon in a conic, Math. Gaz. 51 (May 1967) pp. 150–152.CrossRefGoogle Scholar
2. Wilkinson, T. T. Mathematical questions with their solutions, 2015, Educational Times 17 (1872) p.72.Google Scholar
3. Coxeter, H. S. M. and Greitzer, S. L. Geometry revisited, Mathematical Association of America (1967).Google Scholar
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