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Trigonometry and Fibonacci numbers

Published online by Cambridge University Press:  01 August 2016

Barry Lewis
Barry Lewis*
Affiliation:
Flat 1, 110 Highgate Hill, London N6 5HE, e-mail: barry@mathscounts.org
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Extract

This article sets out to explore some of the connections between two seemingly distinct mathematical objects: trigonometric functions and the integer sequences composed of the Fibonacci and Lucas numbers. It establishes that elements of Fibonacci/Lucas sequences obey identities that are closely related to traditional trigonometric identities. It then exploits this relationship by converting existing trigonometric results into corresponding Fibonacci/Lucas results. Along the way it uses mathematical tools that are not usually associated with either of these objects.

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Type
Articles
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The Mathematical Gazette , Volume 91 , Issue 521 , July 2007, pp. 216 - 226
Copyright
Copyright © The Mathematical Association 2007

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References

1. Fisk, S., The Fibonacci Quarterly 1 (April 1963) p. 85.Google Scholar
2. Taylor, L., The Fibonacci Quarterly 20 (November 1982) p. 369.Google Scholar
3. Gow, M., A course in pure mathematics, Edward Arnold (1992), p. 166, Question 28 (i).Google Scholar