Forma, Vol. 19 (No. 4), pp. 335-354, 2004

Growth in Plants: A Study in Number

Jay Kappraff

New Jersey Institute of Technology, Department of Mathematics, Newark, NJ 07102, U.S.A.
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(Received March 11, 2005; Accepted March 18, 2005)

Keywords: Phyllotaxis, Fibonacci Numbers, Golden Mean, Continued Fractions, Farey Series, Wythoff's Game, Zeckendorf Notation

Abstract. Three models of plant phyllotaxis are presented. Phyllotaxis is shown to be governed by subtle properties of number which insure that the florets are arranged so as to have the most space and therefore have the greatest access to sunlight. The mathematical tools discussed are Farey series, Wythoff's game, continued fractions, and a Fibonacci number system called Zeckendorf notation.

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