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Symmetry: Culture and Science
Volume 32, Number 1, pages 025-040 (2021)
https://doi.org/10.26830/symmetry_2021_1_025

PHI-BONACCI IN ANCIENT GREECE

Johan Gielis1,2

1 Department of Biosciences Engineering, University of Antwerp, 171 Groenenborgerlaan, Antwerp, 2020, Belgium.
2 Geniaal BV, 8 Nottebohmstraat, Antwerp, 2018, Belgium.
E-mail: johan.gielis@uantwerpen.be
ORCID: 0000-0002-4536-3839

Abstract: Fibonacci numbers are a very popular subject in mathematics, culture and science. A major open question is why the ancient Greeks overlooked this series, while they were very familiar with the golden mean and division in extreme—and mean—ratio. Furthermore, they could compute the square root of five to a high degree of precision using Theon’s ladder. This fact is based on tables built with side and diagonal numbers, and it is a simple and incredibly efficient method to compute roots of integers, though it is little known even now among most of the experts. The biologist D’Arcy Wentworth Thompson showed that the same method could be used to generate the Fibonacci series using a simple shift in the computation of the tables. He argues, quite convincingly, that the ancient Greeks could not have overlooked this. Actually, the same method can be used to generate all possible regular phyllotaxis patterns.

Keywords: Fibonacci, square roots, Theon, Theodorus.

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