mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without...
5 KB (589 words) - 15:01, 15 August 2024
are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional...
49 KB (6,295 words) - 22:27, 12 July 2024
mathematics, a stuck unknot is a closed polygonal chain in three-dimensional space (a skew polygon) that is topologically equal to the unknot but cannot be deformed...
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Jones polynomial (section Detection of the unknot)
polynomial is characterized by taking the value 1 on any diagram of the unknot and satisfies the following skein relation: ( t 1 / 2 − t − 1 / 2 ) V (...
17 KB (2,339 words) - 23:46, 13 August 2024
distinguishes the trefoil from the unknot. The simplest such invariant is tricolorability: the trefoil is tricolorable, but the unknot is not. In addition, virtually...
9 KB (1,239 words) - 08:07, 2 November 2023
less than or equal to 4π, then K is an unknot, i.e.: If ∮ K | κ ( s ) | d s ≤ 4 π , then K is an unknot . {\displaystyle {\text{If}}\ \oint _{K}|\kappa...
4 KB (412 words) - 22:51, 17 October 2022
Unsolved problem in mathematics: Can unknots be recognized in polynomial time? (more unsolved problems in mathematics) In mathematics, the unknotting...
12 KB (1,374 words) - 08:36, 28 May 2024
(King Crimson album) knotwork (Discipline Global Mobile logo) Endless knot (unknot) Eternity knot Fan knot Fiador knot Flat mat knot Flores button knot Friendship...
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the ends together. (That is, a twist knot is any Whitehead double of an unknot.) The twist knots are an infinite family of knots, and are considered the...
3 KB (466 words) - 05:58, 4 August 2021
of components is gcd(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial...
16 KB (1,790 words) - 13:16, 27 July 2024
rings (63 2) L10a140 Satellite Composite knots Granny Square Knot sum Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22...
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it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure-eight knot is a prime knot. The name is...
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further negative supercoiling like the latter enzyme. Topoisomerase IV can unknot right-handed knots and decatenate right-handed catenanes without acting...
3 KB (375 words) - 21:08, 29 March 2021
is not actually knotted, it would in topological terms be considered an unknot. In Norwegian heraldry a Bowen knot is called a valknute (valknut) and the...
4 KB (480 words) - 00:28, 20 August 2024
The unknot is not equivalent to the trefoil knot since one cannot be deformed into the other through a continuous path of homeomorphisms of the ambient...
23 KB (3,271 words) - 09:41, 30 July 2024
knots from each other. However, there are invariants which distinguish the unknot from all other knots, such as Khovanov homology and knot Floer homology...
10 KB (1,269 words) - 23:58, 31 January 2023
simplest knot, called the unknot or trivial knot, is a round circle embedded in R3. In the ordinary sense of the word, the unknot is not "knotted" at all...
23 KB (2,508 words) - 21:20, 11 January 2024
number of Reidemeister moves required to change a diagram of the unknot to the standard unknot. In detail, for any such diagram with c {\displaystyle c} crossings...
8 KB (927 words) - 13:21, 11 September 2021
one component is called the Hopf link, which consists of two circles (or unknots) linked together once. The circles in the Borromean rings are collectively...
8 KB (1,107 words) - 01:03, 25 April 2024
first diagram is two unknots with four crossings. Patching the latter P() = A × P() + P() gives, again, a trefoil, and two unknots with two crossings (the...
8 KB (931 words) - 20:32, 11 February 2024
as well. The standard Möbius strip has the unknot for a boundary but is not a Seifert surface for the unknot because it is not orientable. The "checkerboard"...
10 KB (1,358 words) - 07:56, 18 July 2024
t ) = 1 {\displaystyle {\begin{aligned}P_{n}(unknot)&=q^{n-1}+q^{n-3}+\cdots +q^{1-n}&&n>0\\P_{0}(unknot)&=1\end{aligned}}} For n > 1 {\displaystyle n>1}...
11 KB (1,464 words) - 23:17, 22 May 2024
limited edition includes the DVD of the live performance of the one-man tour "Unknot/Reknot" held at Zepp DiverCity (Tokyo) on October 15, 2022. On June 26,...
18 KB (1,320 words) - 12:03, 3 August 2024
links. See also list of knots, list of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot - (2,3)-torus knot...
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property of having the same Alexander polynomial and Conway polynomial as the unknot. The issue of the sliceness of the Conway knot was resolved in 2020 by Lisa...
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not simply-connected. The conjecture states that all knots, except the unknot, have Property P. Research on Property P was started by R. H. Bing, who...
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into its mirror image, otherwise it is called chiral. For example, the unknot and the figure-eight knot are achiral, whereas the trefoil knot is chiral...
33 KB (3,803 words) - 14:32, 2 August 2024
A chart of all prime knots with seven or fewer crossings, not including mirror-images, plus the unknot (which is not considered prime)....
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shares a Jones polynomial. It has the same Alexander polynomial as the unknot. Weisstein, Eric W. "Conway's Knot". mathworld.wolfram.com. Retrieved 2020-05-19...
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In R 3 {\displaystyle \mathbb {R} ^{3}} , the unknot is not ambient-isotopic to the trefoil knot since one cannot be deformed into the other through a...
2 KB (224 words) - 22:23, 24 March 2024