Editing Phyllotaxis (section)

== Repeating spiral ==
The rotational angle from leaf to leaf in a repeating spiral can be represented by a fraction of a [[full rotation]] around the stem.

Alternate distichous leaves will have an angle of 1/2 of a full rotation. In [[beech]] and [[hazel]] the angle is 1/3,{{Citation needed|date=December 2022|reason = in hazel (Corylus avellana) this is only true for vertical twigs; horizontal twigs are alternate distichous. Need a more detailed (and perhaps more botanical) source that covers this.}} in [[oak]] and [[apricot]] it is 2/5, in [[sunflowers]], [[Populus|poplar]], and [[pear]], it is 3/8, and in [[willow]] and [[almond]] the angle is 5/13.<ref>{{Cite book|title=Introduction to geometry|first=H. S. M. |last=Coxeter| name-list-style = vanc |author-link =Harold Scott MacDonald Coxeter|publisher =Wiley|year=1961|pages=169}}</ref> The numerator and denominator normally consist of a [[Fibonacci number]] and its second successor. The number of leaves is sometimes called rank, in the case of simple Fibonacci ratios, because the leaves line up in vertical rows. With larger Fibonacci pairs, the pattern becomes complex and non-repeating. This tends to occur with a basal configuration. Examples can be found in [[Asteraceae|composite]] [[flower]]s and [[seed]] heads. The most famous example is the [[sunflower]] head. This phyllotactic pattern creates an optical effect of criss-crossing spirals. In the botanical literature, these designs are described by the number of counter-clockwise spirals and the number of clockwise spirals. These also turn out to be [[Fibonacci numbers]]. In some cases, the numbers appear to be multiples of Fibonacci numbers because the spirals consist of whorls.