Tools that can be forced between parts of the knot ( such as picks and marlinespikes ) may help.

5 feet 6 or 8 inches high, weighs between 150 and 160 pounds, rather bright complexion, but not a mulatto, broad shoulders, larger flat nose, large eyes, broad flat feet, rather knockneed, walks brisk and active, hair on the top of the head very thin, no beard, except on the upper lip and the top of the chin, a scar on one of his temples, also one on the back of his neck, a large knot on one of the bones of his right arm, near the wrist, produced by a blow.

The symmetry between and in the Jones polynomial reflects the fact that the figure-eight knot is achiral.

The discovery of the Jones polynomial by Vaughan Jones in 1984, and subsequent contributions from Edward Witten, Maxim Kontsevich, and others, revealed deep connections between knot theory and mathematical methods in statistical mechanics and quantum field theory.

Pearls are threaded onto silk, and a knot is tied between each one to not only space them for greater individual prominence but to also keep them from rubbing directly against each other and risking the abrasion of the nacre that gives them their luster.

* Link concordance, a relation between mathematical links in knot theory

** windsor collar or spread collar — a dressier collar designed with a wide distance between points ( the spread ) to accommodate the windsor knot tie.

Neckties are traditionally worn with the top shirt button fastened, and the tie knot resting comfortably between the collar points.

The individual knot values are not meaningful by themselves ; only the ratios of the difference between the knot values matter.

Among the central threads running through de Man's work is his attempt to tease out the tension between rhetoric ( which in de Man's usage tends to mean figural language and trope ) and meaning, seeking out moments in the text where linguistic forces " tie themselves into a knot which arrests the process of understanding.

Informally, a skein relation gives a linear relation between the values of a knot polynomial on a collection of three links which differ from each other only in a small region.

Pullin, Gambini, and Bernd Brügman also wrote a series of papers that make an important connection between knot theory and quantum gravity, by showing that the Jones polynomial can be used to solve a quantum form of Einstein's equations.

A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot.

Though the trefoil knot is chiral, it is also invertible, meaning that there is no distinction between a counterclockwise-oriented trefoil and a clockwise-oriented trefoil.

Looking at the development of topological quantum field theory we should be consider that it has a lot of applications to Seiberg-Witten gauge theory, topological string theory, the relationship between knot theory and quantum theory, and quantum knot invariants.

On 1 June 1965, reporter Roy Smith described plans for the then unbuilt junction as a " cross between a plate of spaghetti and an unsuccessful attempt at a Staffordshire knot ", and a sub-editor captioned the article " Spaghetti Junction ".

It is very comfortable to wear, as the knot itself will hold the tie firmly in place while still keeping space between the collar and the neck.

Vaughan Jones ' discovery of the Jones polynomial in the early 1980s not only led knot theory in new directions but gave rise to still mysterious connections between low-dimensional topology and mathematical physics.

The knot balances the load between the two hitches, and is used in wharfs and docks.

The territory was also important for Romans as a communication knot between northern Hispania and southwestern Gallia.

In an article published in the Birmingham Evening Mail on 1 June 1965 the journalist Roy Smith described plans for the junction as " like a cross between a plate of spaghetti and an unsuccessful attempt at a Staffordshire knot ", with the headline above the article on the newspaper's front page reading " Spaghetti Junction ".

It lies close to Biel, at the boundary between French-and German-speaking regions, and at a knot of highways.

Though these properties are well suited to fishing, there are other knots which may provide superior performance, such as the blood knot.

For example, he was able to show that all but ten Dehn surgeries on the figure-eight knot resulted in non-Haken, non-Seifert-fibered irreducible 3-manifolds ; these were the first such examples.

Historically, many of the early knot invariants are not defined by first selecting a diagram but defined intrinsically, which can make computing some of these invariants a challenge.

* Umbilical cord compression can result from, for example, entanglement of the cord, a knot in the cord, or a nuchal cord, ( which is when the umbilical cord becomes wrapped around the fetal neck ) but these conditions do not always cause obstruction of fetal circulation.

In the special case in which M is the 3-sphere, Witten has shown that these normalized correlation functions are proportional to known knot polynomials.

Consider a planar projection of each knot and suppose these projections are disjoint. Find a rectangle in the plane where one pair of sides are arcs along each knot but is otherwise disjoint from the knots.

# Consider a planar projection of each knot and suppose these projections are disjoint.

The six months elapsed without any solution being produced ; but he received a letter from Leibniz, stating that he had " cut the knot of the most beautiful of these problems ," and requesting that the period for their solution should be extended to Christmas next ; that the French and Italian mathematicians might have no reason to complain of the shortness of the period.

First created in the second half of the 16th-century, these terraces would originally have included a number of knot gardens, probably with Italianate sculpture and carved stone balustrades.

The visual form of these curves is often suggestive of a three-dimensional knot, and indeed many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures.

In particular, the knot can be formed with an end of the rope, in a closed loop or strap, or a combination of these two in which it is tied with the end and then formed into a loop by securing the free end to the standing part.

Since the Wirtinger presentation has one generator for each strand in a knot diagram, these invariants can be computed by counting ways of labelling each strand by an element of, subject to certain constraints.

This design has been considered by others as well, such as the Monomaran designs by " The 40 knot Sailboat " author Bernard Smith, and these designs been called 3-point proas by some, a reference to the 3 point hulls used in hydroplanes.

between these lines ; one can project these to form a tangle diagram, analogous to a knot diagram.

* The square knot and the granny knot have isomorphic knot groups, yet these two knots are inequivalent.

There are many examples of these, such as the complement of a figure 8 knot or the Seifert – Weber space.

There are a limited number of applications that involve repeated shock loads to the knot and in these 4 wraps are usually sufficient.

But these initial failures can reform the knot tighter, if the ends are long enough to avoid passing into the knot.

To raise and lower cargo they used large blocks and these required a larger stopper knot to prevent the line from running completely through the block.

Since two distinct variations of the rolling hitch are widely referred to by the same name, and Magnus hitch now may refer to a different knot than it used to, the use of Ashley reference numbers for these related hitches can eliminate ambiguity when required.