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| {{Infobox knot theory
| | Name: Cecile Whitlow<br>Age: 18<br>Country: Australia<br>Town: Valencia Creek <br>Post code: 3860<br>Street: 26 Settlement Road<br><br>My blog [http://www.olwallpaper.com/profile/baprenderg type my essay] |
| | name= Stevedore knot
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| | practical name= Stevedore knot
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| | image= Blue Stevedore Knot.png
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| | caption=
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| | arf invariant= 0
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| | braid length= 7
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| | braid number= 4
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| | bridge number= 2
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| | crosscap number= 2
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| | crossing number= 6
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| | hyperbolic volume= 3.16396
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| | linking number=
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| | stick number= 8
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| | unknotting number= 1
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| | conway_notation= [42]
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| | ab_notation= 6<sub>1</sub>
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| | dowker notation= 4, 8, 12, 10, 2, 6
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| | thistlethwaite=
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| | last crossing= 5
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| | last order= 2
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| | next crossing= 6
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| | next order= 2
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| | alternating= alternating
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| | class= hyperbolic
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| | fibered=
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| | prime= prime
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| | slice= slice
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| | symmetry= reversible
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| | pretzel= pretzel
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| | tricolorable=
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| | twist= twist
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| }}
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| [[Image:Double eight -1.JPG|thumb|The common [[stevedore knot]]. If the ends were joined together, the result would be equivalent to the mathematical knot.]]
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| In [[knot theory]], the '''stevedore knot''' is one of three [[prime knot]]s with [[crossing number (knot theory)|crossing number]] six, the others being the [[6₂ knot|6<sub>2</sub> knot]] and the [[6₃ knot|6<sub>3</sub> knot]]. The stevedore knot is listed as the '''6<sub>1</sub> knot''' in the [[Alexander–Briggs notation]], and it can also be described as a [[twist knot]] with four twists, or as the (5,−1,−1) [[pretzel link|pretzel knot]].
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| The mathematical stevedore knot is named after the common [[stevedore knot]], which is often used as a [[stopper knot|stopper]] at the end of a [[rope]]. The mathematical version of the knot can be obtained from the common version by joining together the two loose ends of the rope, forming a knotted [[loop (topology)|loop]].
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| The stevedore knot is [[invertible knot|invertible]] but not [[amphichiral knot|amphichiral]]. Its [[Alexander polynomial]] is
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| :<math>\Delta(t) = -2t+5-2t^{-1}, \,</math> | |
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| its [[Conway polynomial]]{{dn|date=January 2014}} is
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| :<math>\nabla(z) = 1-2z^2, \, </math> | |
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| and its [[Jones polynomial]] is
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| :<math>V(q) = q^2-q+2-2q^{-1}+q^{-2}-q^{-3}+q^{-4}. \, </math><ref>{{Knot Atlas|6_1}}</ref> | |
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| The Alexander polynomial and Conway polynomial are the same as those for the knot 9<sub>46</sub>, but the Jones polynomials for these two knots are different.<ref>{{MathWorld|title=Stevedore's Knot|urlname=StevedoresKnot}}</ref> Because the Alexander polynomial is not [[monic polynomial|monic]], the stevedore knot is not [[fibered knot|fibered]].
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| The stevedore knot is a [[ribbon knot]], and is therefore also a [[slice knot]].
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| The stevedore knot is a [[hyperbolic knot]], with its complement having a [[Hyperbolic volume (knot)|volume]] of approximately 3.16396.
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| ==See also==
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| * [[Figure-eight knot (mathematics)]]
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| ==References==
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| {{reflist}}
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| {{Knot theory|state=collapsed}}
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| {{knottheory-stub}}
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Name: Cecile Whitlow
Age: 18
Country: Australia
Town: Valencia Creek
Post code: 3860
Street: 26 Settlement Road
My blog type my essay