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On the mystery of the golden angle in phyllotaxis
Author(s) -
KING S.,
BECK F.,
LÜTTGE U.
Publication year - 2004
Publication title -
plant, cell and environment
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.646
H-Index - 200
eISSN - 1365-3040
pISSN - 0140-7791
DOI - 10.1111/j.1365-3040.2004.01185.x
Subject(s) - phyllotaxis , golden ratio , fibonacci number , divergence (linguistics) , mathematics , irrational number , maxima and minima , section (typography) , shadow (psychology) , maxima , series (stratigraphy) , geometry , mathematical analysis , combinatorics , botany , biology , paleontology , computer science , operating system , psychology , art , linguistics , philosophy , shoot , performance art , meristem , psychotherapist , art history
Phyllotaxis, the arrangement of leaves around a stem, shows in the vast majority of cases a regularity in the divergence angle of subsequent leaves which divide the whole circle into regular fractions. These are in most cases rational fractions of two Fibonacci numbers in an alternating series, converging towards the irrational limit of the golden section, corresponding to the golden divergence angle of 137.5 . . . degrees. This peculiarity was a long‐standing mystery. Here, it is related to the evolutionary pressure of optimal light capture for maximal photosynthetic activity. A model is established which relates minimal shadowing for the lower leaves to the divergence angle. Numerical results of this model agree well with semi‐empirical data on the dependence of light capture from the divergence angle. The basic shadow function of the model is also related with the demand of minimal shadowing for the angular separation of leaves and obtain, using elementary number theory, as solution the golden section. Further numerical studies show that the rational approach to the golden section (Schimper–Braun series) is related to the leaf width and the number of leaves of the plant.