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...

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...

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...

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 (...

distinguishes the trefoil from the unknot. The simplest such invariant is tricolorability: the trefoil is tricolorable, but the unknot is not. In addition, virtually...

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...

Unsolved problem in mathematics: Can unknots be recognized in polynomial time? (more unsolved problems in mathematics) In mathematics, the unknotting...

(King Crimson album) knotwork (Discipline Global Mobile logo) Endless knot (unknot) Eternity knot Fan knot Fiador knot Flat mat knot Flores button knot Friendship...

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...

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"...

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...

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...

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...

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...

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...

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...

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...

further negative supercoiling like the latter enzyme. Topoisomerase IV can unknot right-handed knots and decatenate right-handed catenanes without acting...

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...

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...

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}...

A chart of all prime knots with seven or fewer crossings, not including mirror-images, plus the unknot (which is not considered prime)....

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,...

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...

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...

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...

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...

(ISBN 0-8048-0644-6). This book includes Zen texts, but also the Vijnana Bhairava Tantra Unknot The World In You. His second book, which published through Sequoia University...

knots to the hyperbolic geometry of their complements. Let O denote the unknot. For any knot K {\displaystyle K} , let ⟨ K ⟩ N {\displaystyle \langle K\rangle...

conjectures in stable homotopy theory to be resolved. Unknotting problem: can unknots be recognized in polynomial time? Volume conjecture relating quantum invariants...