Editing Phyllotaxis (section)

== History ==
{{see also|Patterns in nature#History}}
Some early scientists—notably [[Leonardo da Vinci]]—made observations of the spiral arrangements of plants.<ref>{{cite book |author=Leonardo da Vinci |author-link=Leonardo da Vinci |editor-last=Taylor |editor-first=Pamela |title=The Notebooks of Leonardo da Vinci |publisher=New American Library|year=1971|page=121}}</ref> In 1754, [[Charles Bonnet]] observed that the spiral phyllotaxis of plants were frequently expressed in both [[clockwise]] and counter-clockwise [[golden ratio]] series.<ref name=livio110>{{cite book|last=Livio|first=Mario|author-link=Mario Livio|title=The Golden Ratio: The Story of Phi, the World's Most Astonishing Number|url=https://books.google.com/books?id=bUARfgWRH14C|orig-year=2002|edition=First trade paperback|year=2003|publisher=[[Random House|Broadway Books]]|location=New York City|isbn=978-0-7679-0816-0|page=110}}</ref> Mathematical observations of phyllotaxis followed with [[Karl Friedrich Schimper]] and his friend [[Alexander Braun]]'s 1830 and 1830 work, respectively; [[Auguste Bravais]] and his brother Louis connected phyllotaxis ratios to the [[Fibonacci sequence]] in 1837.<ref name=livio110/>

Insight into the mechanism had to wait until [[Wilhelm Hofmeister]] proposed a model in 1868. A [[primordium]], the nascent leaf, forms at the least crowded part of the shoot [[meristem]]. The [[golden angle]] between successive leaves is the blind result of this jostling. Since three golden arcs add up to slightly more than enough to wrap a circle, this guarantees that no two leaves ever follow the same radial line from center to edge. The generative spiral is a consequence of the same process that produces the clockwise and counter-clockwise spirals that emerge in densely packed plant structures, such as ''[[Protea]]'' flower disks or pinecone scales.

In modern times, researchers such as [[Mary Snow]] and George Snow<ref>{{cite journal |author1=Snow, M. |author2=Snow, R. |year=1934 |title=The interpretation of Phyllotaxis |journal=Biological Reviews |volume=9 |issue=1 |pages=132–137 |doi=10.1111/j.1469-185X.1934.tb00876.x|s2cid=86184933 }}</ref> continued these lines of inquiry. Computer modeling and morphological studies have confirmed and refined Hoffmeister's ideas. Questions remain about the details. Botanists are divided on whether the control of leaf migration depends on chemical [[gradient]]s among the [[Primordium|primordia]] or purely mechanical forces. [[Lucas number]]s rather than Fibonacci numbers have been observed in a few plants<ref>{{Cite book |last=Church |first=Arthur Harry |url=https://books.google.com/books?id=9cdJAQAAMAAJ&dq=Church,+A.H.+(1904).+On+the+Relation+of+phyllotaxis+to+mechanical+laws.+Williams+and+Norgate,+London.&pg=PA109 |title=On the Relation of Phyllotaxis to Mechanical Laws |date=1904 |publisher=Williams & Norgate |pages=198 |language=en}}</ref> and occasionally, the leaf positioning appears to be random.{{citation needed|date=March 2023}}