## FIBONACCI SERIES
^{2)}^{4)}^{5)}

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An additive series of consecutive numbers whose ratios develop in the following way

This series was introduced by the Italian mathematician FIBONACCI in 1220.

As can be observed, every successive term of the progression 1, 1, 2, 3, 5, 8, 13, etc,… is the sum of the two former ones.

On the other hand, the limit of the ratio's sequence is √5+1)/2 = 1,618…, the so-called golden section.

Both the series and the golden section appear in numerous natural structures and seem to reflect opposite constraints in field dynamics. It thus reflects and explains the genesis of specific forms, as already shown for example by SCHIMPER, BRAUN and BRAVAIS for plants, in the 19th Century. It is also implicit in d'Arcy W. THOMPSON's "Growth and Form" (1916).

Its use in systemic modelling could probably be much developed. A.A DAVYDOV published in 1992 a very stimulating paper on this subject: "Theory of Harmony of Proportions and Functions in Social Systems" (1992).

### Categories

- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented

### Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

* Bertalanffy Center for the Study of Systems Science (2020).* Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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