Editing Spiral (section)

==In nature==
The study of spirals in [[nature]] has a long history. [[Christopher Wren]] observed that many [[Exoskeleton|shells]] form a [[logarithmic spiral]]; [[Jan Swammerdam]] observed the common mathematical characteristics of a wide range of shells from ''[[Helix (genus)|Helix]]'' to ''[[Spirula]]''; and [[Henry Nottidge Moseley]] described the mathematics of [[univalve]] shells. [[D'Arcy Wentworth Thompson|D’Arcy Wentworth Thompson]]'s ''[[On Growth and Form]]'' gives extensive treatment to these spirals. He describes how shells are formed by rotating a closed curve around a fixed axis: the [[shape]] of the curve remains fixed, but its size grows in a [[geometric progression]]. In some shells, such as ''[[Nautilus]]'' and [[ammonite]]s, the generating curve revolves in a plane perpendicular to the axis and the shell will form a planar discoid shape. In others it follows a skew path forming a [[helix|helico]]-spiral pattern. Thompson also studied spirals occurring in [[Horn (anatomy)|horn]]s, [[teeth]], [[claw]]s and [[plant]]s.<ref>{{Cite book|first=D'Arcy|last=Thompson|title=On Growth and Form |year=1942 |orig-year=1917 |url=https://archive.org/details/ongrowthform00thom |publisher=Cambridge : University Press ; New York : Macmillan| pages=748–933}}</ref>

A model for the pattern of [[floret]]s in the head of a [[sunflower]]<ref>{{cite web|url=https://www.geogebra.org/m/B4C9bbuy|title=Geogebra: Sunflowers are Irrationally Pretty|author=Ben Sparks}}</ref> was proposed by H. Vogel. This has the form
:<math>\theta = n \times 137.5^{\circ},\ r = c \sqrt{n}</math>
where ''n'' is the index number of the floret and ''c'' is a constant scaling factor, and is a form of [[Fermat's spiral]]. The angle 137.5° is the [[golden angle]] which is related to the [[golden ratio]] and gives a close packing of florets.<ref>{{cite book | last =Prusinkiewicz | first =Przemyslaw | author-link =Przemyslaw Prusinkiewicz | author2 =Lindenmayer, Aristid | author-link2 =Aristid Lindenmayer | title =The Algorithmic Beauty of Plants | publisher =Springer-Verlag | year =1990 | pages =[https://archive.org/details/algorithmicbeaut0000prus/page/101 101–107] | url =https://archive.org/details/algorithmicbeaut0000prus/page/101 | isbn =978-0-387-97297-8 }}</ref>

Spirals in plants and animals are frequently described as [[whorl (botany)|whorls]]. This is also the name given to spiral shaped [[fingerprint]]s.

<gallery widths="220" heights="160">
The center Galaxy of Cat's Eye.jpg|An artist's rendering of a spiral galaxy.
Helianthus whorl.jpg|Sunflower head displaying florets in spirals of 34 and 55 around the outside.
</gallery>