FIBONACCI SERIES
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1263 ▶ |
| Object type | Discipline oriented, Human sciences, Methodology or model |
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 succesive 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 ($Template:Ency sqrt$+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).