Abstract
Assuming that neither the Fibonacci sequence nor any numerical ratio or angular deflection is specified in the genetic material of a plant cell, there must be an arranging mechanism effecting the sequence mentioned. Considering the ubiquity of the Fibonacci numbers in nature, embracing many species of flora, we expect a very simple geometrical law to be responsible. Success in finding such a law does not constitute a proof, but it is at the least an indication that we should look here with mathematical rather than biological eyes. The idea may seem self-evident. However, in the literature it has not yet been honored as the basis for constructing the phyllotaxis in centric, planar models. It is shown here that for the construction of a phyllotactic structure, no special angles or distances need be defined; natural growth functions can be used; planar, cylindrical, conical, and paraboloid constructions are possible within the same model; and constructions leading to accessory sequences and multijugate sequences can also be carried out.
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