- Fermat's spiral
**Fermat's spiral**(also known as a parabolicspiral ) follows the equation:$r\; =\; pm\; heta^\{1/2\},$

in

polar coordinates (the more general Fermat's spiral follows "r"^{ 2}= "a"^{ 2}"θ".) It is a type ofArchimedean spiral . [*mathworld|urlname=FermatsSpiral |title=Fermat Spiral*]In disc

phyllotaxis (sunflower , daisy), the mesh of spirals occurs inFibonacci number s because divergence (angle of succession in a single spiral arrangement) approaches thegolden ratio . The shape of the spirals depends on the growth of the elements generated sequentially. In mature-discphyllotaxis , when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. The full model proposed by H Vogel in 1979 [*Citation*] is

last =Vogel

first =H

title =A better way to construct the sunflower head

journal =Mathematical Biosciences

issue =44

pages =179–189

year =1979:$r\; =\; c\; sqrt\{n\},$

:$heta\; =\; n\; imes\; 137.508^circ,$

where "θ" is the angle, "r" is the radius or distance from the center, and "n" is the index number of the floret and "c" is a constant scaling factor. The angle 137.5° is the

golden angle which is approximated by ratios of Fibonacci numbers. [*cite book*]

last =Prusinkiewicz

first =Przemyslaw

authorlink =Przemyslaw Prusinkiewicz

coauthors =Lindenmayer, Aristid

title =The Algorithmic Beauty of Plants

publisher =Springer-Verlag

date =1990

location =

pages =101–107

url =http://algorithmicbotany.org/papers/#webdocs

doi =

id = ISBN 978-0387972978**References**jordan ratliff

**References***

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