Visibility in a pure model of golden spiral phyllotaxis

This paper considers the geometry of plants with golden spiral phyllotaxis, i.e. growing leaf by leaf on a spiral with golden divergence angle, via the simplest mathematical model, a cylinder with regular arrangement of points on its surface. As is well-known, Fibonacci numbers appear by means of the order of parastichies. This fact is shown to be a straightforward application of logical consequences to a particular model with respect to pure visibility. This notion is very similar to that of contact parastichies. The 3-D cylindrical model of golden spiral phyllotaxis abstracts from the form of leaves and identifies them with points. Pure visibility is specified in the 2-D representation so that common sense parastichies can be scrutinized. The main Theorem states that the orders of the purely most visible parastichies are Fibonacci numbers.