Part I deals with the descriptive aspects of phyllotaxis – in its centric, cylindrical, and hierarchical representations. The parameters defining phyllotactic patterns have been introduced, and what is called here the fundamental theorem of phyllotaxis has been presented. This theorem should be in the very core of every teaching curriculum on the rudiments of phyllotaxis, whether it be in a botany or in a mathematical classroom. That is why it has been also given an intuitive presentation and applications. This phyllotactic theorem has been and will be frequently encountered.

The proofs of Equations (1.5) to (1.9), and of Richards's formula (4.30) for the centric representation have been made in the context of the cylindrical representation in Chapter 4. The treatment of the cylindrical lattice has been given in the interval [−0.5, +0.5]. This interval makes it easier to identify the visible opposed parastichy pairs. From past experiences the usual interval [0,1] proved to be sometimes confusing with respect to this identification. A definition of visible pair of spirals has been proposed, which generalizes the notion of visible point introduced by Hardy and Wright, and which brought more general results (e.g., the general form of the fundamental theorem of phyllotaxis in Section 2.3.1 and Proposition A4.1 in Appendix 4).

That phyllotactic patterns are fundamentally branched structures, control hierarchies, has been illustrated.