# Flype

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{{Short description|Operation on a knot}}
170px|thumb|A flype consists of turning a tangle, '''T''', by 180 degrees.
In the [mathematical theory of knots](/source/knot_theory), a '''flype''' is a kind of manipulation of knot and [link diagram](/source/knot_diagram)s 
used in the [Tait flyping conjecture](/source/Tait_conjectures).
It consists of twisting a part of a knot, a [tangle](/source/tangle_(knot_theory)) '''T''', by 180 degrees. Flype comes from a [Scots](/source/Scots_language) word meaning ''to fold'' or ''to turn back'' ("as with a sock").<ref name="htw">{{citation
 |last1       = Hoste
 |first1      = Jim
 |last2       = Thistlethwaite
 |first2      = Morwen
 |last3       = Weeks
 |first3      = Jeff
 |doi         = 10.1007/BF03025227
 |issue       = 4
 |journal     = The Mathematical Intelligencer
 |mr          = 1646740
 |pages       = 33–48
 |title       = The first 1,701,936 knots
 |url         = http://www.math.harvard.edu/~ctm/home/text/class/harvard/101/05/html/home/pdf/first.pdf
 |volume      = 20
 |year        = 1998
 |url-status     = dead
 |archiveurl  = https://web.archive.org/web/20131215102511/http://www.math.harvard.edu/~ctm/home/text/class/harvard/101/05/html/home/pdf/first.pdf
 |archivedate = 2013-12-15
}}. Tait used the term to mean, "a change of infinite complementary region").</ref><ref>{{MathWorld|Flype|Flype}}</ref> Two reduced alternating diagrams of an [alternating link](/source/alternating_link) can be transformed to each other using flypes. This is the [Tait flyping conjecture](/source/Tait_flyping_conjecture), proven in 1991 by [Morwen Thistlethwaite](/source/Morwen_Thistlethwaite) and [William Menasco](/source/William_Menasco).<ref>{{MathWorld|TaitsKnotConjectures|Tait's Knot Conjectures}}</ref> 

==See also==
* [Reidemeister move](/source/Reidemeister_move)s are another commonly studied kind of manipulation to knot diagrams.

==References==
{{reflist}}

{{Knot theory}}

Category:Knot operations

{{knottheory-stub}}

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