Notes

1These two relations can be shown easily by induction considering that they are true, then calculating [\tau^{u+1}] or [\lambda^{u+1}] using [\tau^2 = 1+\tau] or [\lambda^2 = 1-\lambda].

2It is very usual in the literature to use [\lambda = 1/\tau^2] to describe phyllotaxis. This choice corresponds to the smaller divergence angle. The other choice, done here, is formally simpler and strongly supported by this property: spirals are defined by the rank u of the Fibonacci number; their speeds of rotation around the origin decrease with u and we choose for a generative spiral the first one given by u = 1.

3Delaunay triangulation is such that sites are associated to cover the surface by triangles. It is related to Voronoi decomposition, because the vertices of Voronoi cells are the centres of the triangles, Delaunay and Voronoi decompositions are dual.

4These limits remain the same in phyllotactic tilings on the sphere and on the hyperbolic plane, providing the same [\pi] area for each site. This will be discussed in a further article on phyllotaxis in non-Euclidean geometry.

5Notice that this strip is very similar to the construction of approximants of a quasicrystal using the cut-and-projection method. It is one of the factors that relate phyllotaxis and quasicrystals.