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Fibonacci numbers and trigonometry

Published online by Cambridge University Press:  01 August 2016

Barry Lewis
Barry Lewis*
Affiliation:
21 Muswell Hill Road, London N10 3JB
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Extract

This article started life as an investigation into certain aspects of the Fibonacci numbers, ‘morphed’ seamlessly into the structure of some infinite matrices and finally resolved into a general set of results that link structural aspects of Fibonacci numbers with trigonometric and hyperbolic functions. It is a surprising fact, but while I can find evidence that the link between these areas has been noted in the past, I can find no evidence that the link has been systematically developed.

Type
Articles
Information
The Mathematical Gazette , Volume 88 , Issue 512 , July 2004 , pp. 194 - 204
Copyright
Copyright © The Mathematical Association 2004

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References

1. Vajda, S., Fibonacci & Lucas Numbers, and the Golden Section, Ellis Horwood (1989) pp. 124–126.Google Scholar
2. Pargeter, A. R., Fibonacci goes hyperbolic, Math. Gaz., 85 (November 2001) pp. 476.Google Scholar
3. Graham, R., Knuth, D., Patashnik, O., Concrete Mathematics, Addison-Wesley (2000).Google Scholar
4. Wilf, Herbert, Generatingfunctionology, Academic Press (1994) p. 33. Also available (for free !) from http://www.cis.upenn.edu/~wilf Google Scholar