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{{short description|Family of mathematical knots}} [[Image:Blue 8_1 Knot.png|thumb|right|A twist knot with six half-twists.]] ...

| name= Three-twist knot | image= Blue Three-Twist Knot.png ...

| twist= twist ...in the [[Alexander–Briggs notation]], and it can also be described as a [[twist knot]] with four half twists, or as the (5,−1,−1) [[pretzel lin ...

...le=The knot book: an elementary introduction to the mathematical theory of knots |publisher=American Mathematical Society |location=Providence, Rhode Island ...knot]]. The following table show the unknotting numbers for the first few knots: ...

...around and along the axial curve <math>X</math>. According to Love (1944) twist is defined by ...into ''normalized total torsion'' <math>T \in [0,1)</math> and ''intrinsic twist'' <math>N \in \mathbb{Z}</math> as ...

...name="Kauffman1991">Kauffman, L.H. (1991). "Knots and physics". Series on Knots and Everything. 1. World Scientific. ISBN 978-981-02-0332-1.</ref> The <math>\tau_{U,V}</math> represents the "twist" mapping defined for <math>k</math>-modules <math>U</math> and <math>V</mat ...

| twist= [[Category:Double torus knots and links]] ...

| twist= [[Category:Double torus knots and links]] ...

* [[three-twist knot]] * all knots and links with volume zero ...

...is the total ''twist number'' (or simply ''[[Twist (differential geometry)|twist]]''), the rate of rotation of the ribbon around its axis. * [[Knots and graphs]] ...

...r the NE and SE endpoints or the SW and SE endpoints. One can suppose each twist does not change the diagram inside a disc containing previously created cro ...rtical arcs. A convention is needed to describe a "positive" or "negative" twist. Often, "rational tangle" refers to a list of numbers representing a simple ...

In the [[knot theory|mathematical theory of knots]], '''L10a140''' is the name in the [https://katlas.org/wiki/The_Thistlethw ...ng with the Borromean rings. So if the blue and yellow loops have only one twist along each side, the resulting configuration is the Borromean rings; if the ...

...energy]], i.e., a [[Functional (mathematics)|functional]] on the space of knots. It was discovered by [[Jun O'Hara]], who demonstrated that the energy blo Conjecturally, there is no energy minimizer for composite knots. [[Robert B. Kusner]] and [[John M. Sullivan (mathematician)|John M. Sulliv ...

...math>c_{C_1, C_2} c_{C_2, C_1}=\mathrm{id}_{C_1\otimes C_2}</math>, so our twist must obey <math>\theta_{C_1 \otimes C_2} = \theta_{C_1} \otimes \theta_{C_2 ...link=Vladimir Turaev |first=V.G. |last=Turaev |title=Quantum Invariants of Knots and 3-Manifolds |publisher=de Gruyter |date=2020 |isbn=978-3-11-088327-5 |o ...

...analogous to [[elementary matrices]] for <math>GL_n(\Z)</math> and [[Dehn twist|Dehn twists]] for [[Mapping class group of a surface|mapping class groups o ...concerns the fundamental groups of three-dimensional [[knot (mathematics)|knots]], which can be solved using Nielsen transformations and a method of [[Jame ...

...autical terminology]], wind speeds are normally expressed in [[Knot (unit)|knots]] and wind angles in [[degree (angle)|degree]]s. The craft's point of sail ...m/s (≈78 knots) the speed at 15 m would be ''V'' (15 m) = 49&nbsp;m/s (≈95 knots) with ''p'' = 0.128.<ref> ...

...s section]] is in the shape of an 'N' and would remain an 'N' after a half-twist. This folded strip, three times as long as it is wide, would be long enough ...=Knotting and threading of molecules: Chemistry and chirality of molecular knots and their assemblies|journal=Angewandte Chemie International Edition|volume ...

...tsICzlHVMXGvy_YNwsSAezSjdf6At-O5fwSFky29x5aKS |title=Quantum Invariants of Knots and 3-Manifolds |date=2016-07-11 |publisher=De Gruyter |isbn=978-3-11-04352 ...times 1 = 1 \otimes \tau = \tau</math> and <math>1\otimes 1 =1</math>. The twist values are <math>\theta_1=1</math> and <math>\theta_{\tau}=e^{4\pi i/5}</ma ...

..., two distinct conformations are possible that differ from each other by a twist of 180 degrees of one of the carbons about the double bond. ...above and below their mean plane) and [[Cyclohexane conformation#Boat and twist-boat conformations|boat]] (with two opposite carbons above the plane, and t ...