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arXiv · 1704.02880

Golden Ratio and Phyllotaxis, what is the mathematical link?

François Bergeron·Christophe Reutenauer
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Abstract

Exploiting Markoff's Theory for rational approximations of real numbers, we explicitly link how hard it is to approximate a given number to an idealized notion of growth capacity for plants which we express as a modular invariant function depending on this number. Assuming that our growth capacity is biologically relevant, this allows us to explain in a satisfying mathematical way why the golden ratio occurs in nature.

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François Bergeron, Christophe Reutenauer. 2017-04-04. Golden Ratio and Phyllotaxis, what is the mathematical link?. https://arxiv.org/abs/1704.02880

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