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Church . — The Principles of Phyllotaxis. 
of such intersecting curve systems are not specially studied in an ordinary 
school curriculum, a preliminary sketch of some of their interesting features 
may be excused, since geometrical relationships have clearly no inherent 
connexion with the protoplasmic growth of the plant-shoot, but are merely 
properties of lines and numbers. 
Thus, by taking first, for example, a system in which spiral curves 
of any nature radiate from a central point in such a manner that 5 are 
Fiq. 35, Curve-system (5 + 8): Fibonacci series. A. full contact-cycle of eight members is 
represented by circular primordia. 
turning in one direction and 8 in the other, giving points of intersection 
in a uniform sequence, a system of meshes and points of intersection is 
obtained, and to either of these units a numerical value may be attached. 
That is to say, if any member along the ‘5’ curves be called 1, the next 
inmost member along the same series will be 6, since the whole system 
is made of 5 rows, and this series will be numbered by differences of 5. 
