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[[Image:Fermat's spiral.svg|frame|right|Fermat's spiral]]
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'''Fermat's spiral''' (also known as a [[parabola|parabolic]] [[spiral]]) follows the equation
 
:<math>r = \pm\theta^{1/2}\,</math>
 
in [[polar coordinates]] (the more general Fermat's spiral follows ''r''<sup>&nbsp;2</sup>&nbsp;=&nbsp;''a''<sup>&nbsp;2</sup>''&theta;''.)
It is a type of [[Archimedean spiral#General Archimedean spiral|Archimedean spiral]].<ref>{{mathworld|urlname=FermatsSpiral |title=Fermat Spiral}}</ref>
 
In disc [[phyllotaxis]] ([[sunflower]], daisy), the mesh of spirals occurs in [[Fibonacci number]]s because divergence (angle of succession in a single spiral arrangement) approaches the [[golden ratio]]. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc [[phyllotaxis]], when all the elements are the same size, the shape of the spirals is that of Fermat spirals&mdash;ideally. That is because Fermat's spiral traverses equal [[annulus (mathematics)|annuli]] in equal turns. The full model proposed by H Vogel in 1979<ref>
{{Cite journal
  | last =Vogel
  | first =H
  | title =A better way to construct the sunflower head
  | journal =Mathematical Biosciences
  | issue =44
  | pages =179–189
  | year =1979
  | doi =10.1016/0025-5564(79)90080-4
  | volume =44
  | postscript =<!--None-->
}}</ref> is
 
:<math>r = c \sqrt{n},</math>
 
:<math>\theta = n \times 137.508^\circ,</math>
 
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 137.508° is the [[golden angle]] which is approximated by ratios of [[Fibonacci number]]s.<ref>{{cite book
  | last =Prusinkiewicz
  | first =Przemyslaw
  | authorlink =Przemyslaw Prusinkiewicz
  | coauthors =[[Aristid Lindenmayer|Lindenmayer, Aristid]]
  | title =The Algorithmic Beauty of Plants
  | publisher =Springer-Verlag
  | date =1990
  | location =
  | pages =101&ndash;107
  | url =http://algorithmicbotany.org/papers/#webdocs
  | doi =
  | isbn = 978-0-387-97297-8 }}</ref>
Fermat's spiral has also been found to be an efficient layout for the mirrors of [[concentrated solar power]] plants.<ref>
{{Cite journal
  | last =Noone
  | first =Corey J.
  | last =Torrilhon
  | first =Manuel
  | last =Mitsos
  | first = Alexander
  | title =Heliostat Field Optimization: A New Computationally Efficient Model and Biomimetic Layout
  | journal =Solar Energy
  |date=December 2011
  | doi =10.1016/j.solener.2011.12.007
  | note = In Press
  | postscript =<!--None-->
}}</ref>  
 
[[Image:Sunflower spiral.png|thumb|692px|The pattern of florets produced by Vogel's model (central image). The other two images show the patterns for slightly different values of the angle.]]
{{clear}}
== See also ==
 
* [[Patterns in nature]]
* [[Spiral of Theodorus]]
 
== References ==
{{Reflist}}
 
* {{cite book | author=J. Dennis Lawrence | title=A catalog of special plane curves | publisher=Dover Publications | year=1972 | isbn=0-486-60288-5 | pages=31,186 }}
 
==External links==
* {{springer|title=Fermat spiral|id=p/f038420}}
* [http://jsxgraph.uni-bayreuth.de/wiki/index.php/Fermat's_spiral Online exploration using JSXGraph (JavaScript)]
 
[[Category:Spirals]]

Revision as of 07:05, 25 February 2014

We all wish To lower our weight quick. We wish To look sleek and fit for summer escapades and social outings. The toughest part of any fat reduction system, however, is frequently merely getting the motivation to begin, plus building a strong foundation for success. Because you need to reach a goals, remember that the greatest spot to begin is the beginning.

Simple carbohydrates are found in every white grain productsincluding rice, spaghetti, and rolls, removing them fromyou diet will enable you to lose weight fast and easy.Because they are digested rapidly simple carbs might have youlooking for food more usually, creating it harder for we tolose pounds.

One of the most simple ways to lose weight is to not ever miss a breakfast. The breakfast sets the mood for the day. A wise breakfast will confirm excellent stamina levels throughout the day plus helps you achieve maximum performance at your work.

I am not a fan of celery, however this soup has a whole bunch. I then recalled reading once that takes more calories to burn than to eat. I looked it up online and according to the Urban Legends Reference Pages, it sure is true. Celery is a negative-calorie food. The site says which an eight-inch stalk of celery takes six calories to consume and six to burn. However yet, it can nonetheless fill you up, which makes it terrific to eat to fight cravings. Realizing this leads me to see how this soup diet can really work.

Consuming Fruits plus Vegetables: Consuming green leafy veggies and fruits daily can enable we detoxify the body and the fat inside the body. They are furthermore known lose weight to stimulate the metabolism system which results in fat loss. Various sprouted beans, pulses, legumes, fruits and greens, aid we remain full for longer exiting less possibilities for hogging found on the junk.

There, for example, the populace appeared to get excited over the yearly appearance of seasonal fruits. I saw young reporters on the TV news acting like cheerleaders because they went out to greenhouses, interviewed farmers plus sampled their strawberries in early summer.

If I wish to lose 10lbs pretty quickly, I constantly add 30 minutes of strolling or bicycle riding to my daily schedule. That alone might cause we to get rid of at least one pound of fat a week, causing you to lose weight even quicker.

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