Editing Archimedean spiral (section)

==Applications==
One method of [[squaring the circle]], due to Archimedes, makes use of an Archimedean spiral.  Archimedes also showed how the spiral can be used to [[angle trisection|trisect an angle]]. Both approaches relax the traditional limitations on the use of straightedge and compass in ancient Greek geometric proofs.<ref name=boyer>{{Cite book  | last = Boyer  | first = Carl B.  | title = A History of Mathematics  | publisher = Princeton University Press  | year = 1968 | location =Princeton, New Jersey  | pages = 140–142  | isbn = 0-691-02391-3}}</ref>

[[File:Two moving spirals scroll pump.gif|thumb|upright=0.5|Mechanism of a scroll compressor]]
The Archimedean spiral has a variety of real-world applications. [[Scroll compressor]]s, used for compressing gases, have rotors that can be made from two interleaved Archimedean spirals, [[involute|involutes of a circle]] of the same size that almost resemble Archimedean spirals,<ref>{{Cite web |last=Sakata |first=Hirotsugu |last2=Okuda |first2=Masayuki |title=Fluid compressing device having coaxial spiral members |url=http://www.freepatentsonline.com/5603614.html |access-date=2006-11-25}}</ref> or hybrid curves.

Archimedean spirals can be found in [[spiral antenna]], which can be operated over a wide range of frequencies.

The coils of [[watch]] [[balance spring]]s and the grooves of very early [[gramophone record]]s form Archimedean spirals, making the grooves evenly spaced (although variable track spacing was later introduced to maximize the amount of music that could be cut onto a record).<ref>{{Cite web |last=Penndorf |first=Ron |title=Early Development of the LP |url=http://ronpenndorf.com/journalofrecordedmusic5.html |url-status=dead |archive-url=https://web.archive.org/web/20051105045015/http://ronpenndorf.com/journalofrecordedmusic5.html |archive-date=5 November 2005 |access-date=2005-11-25}}. See the passage on ''Variable Groove''.</ref>

Asking for a patient to draw an Archimedean spiral is a way of quantifying human [[tremor]]; this information helps in diagnosing neurological diseases.

Archimedean spirals are also used in [[digital light processing]] (DLP) projection systems to minimize the "[[rainbow effect]]", making it look as if multiple colors are displayed at the same time, when in reality red, green, and blue are being cycled extremely quickly.<ref>{{citation|title=Handbook for Sound Engineers|first=Glen|last=Ballou|publisher=CRC Press|year=2008|isbn=9780240809694|page=1586|url=https://books.google.com/books?id=zsEBavFYZuEC&pg=PA1586}}</ref> Additionally, Archimedean spirals are used in food microbiology to quantify bacterial concentration through a spiral platter.<ref>{{Cite journal |last=Gilchrist |first=J. E. |last2=Campbell |first2=J. E. |last3=Donnelly |first3=C. B. |last4=Peeler |first4=J. T. |last5=Delaney |first5=J. M. |year=1973 |title=Spiral Plate Method for Bacterial Determination |journal=Applied Microbiology |volume=25 |issue=2 |pages=244–52 |doi=10.1128/AEM.25.2.244-252.1973 |pmc=380780 |pmid=4632851}}</ref>

[[File:Celestial spiral with a twist.jpg|thumb|upright|[[Atacama Large Millimeter Array]] image of [[LL Pegasi]]]]
They are also used to model the pattern that occurs in a roll of paper or tape of constant thickness wrapped around a cylinder.<ref name="uiuc">{{Cite web |last=Peressini |first=Tony |date=3 February 2009 |title=Joan's Paper Roll Problem |url=http://mtl.math.uiuc.edu/special_presentations/JoansPaperRollProblem.pdf |url-status=dead |archive-url=https://web.archive.org/web/20131103150639/http://mtl.math.uiuc.edu/special_presentations/JoansPaperRollProblem.pdf |archive-date=3 November 2013 |access-date=2014-10-06}}</ref><ref name="google">{{Cite book |last=Walser |first=H. |url=https://archive.org/details/symmetry0000wals |title=Symmetry |last2=Hilton |first2=P. |last3=Pedersen |first3=J. |date=2000 |publisher=Mathematical Association of America |isbn=9780883855324 |page=[https://archive.org/details/symmetry0000wals/page/27 27] |access-date=2014-10-06 |url-access=registration}}</ref>

Many dynamic spirals (such as the [[Parker spiral]] of the [[solar wind]], or the pattern made by a [[Catherine wheel (firework)|Catherine's wheel]]) are Archimedean. For instance, the star [[LL Pegasi]] shows an approximate Archimedean spiral in the dust clouds surrounding it, thought to be ejected matter from the star that has been shepherded into a spiral by another companion star as part of a double star system.<ref>{{cite journal
 | last1 = Kim | first1 = Hyosun
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 | last4 = Sahai | first4 = Raghvendra
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 | title = The large-scale nebular pattern of a superwind binary in an eccentric orbit
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