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The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie. In their papers (which are technical) and book (which is for a lay audience, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end.
Knots of diverse colors were used as belts, identity tags, and as a decorative element on instruments. In the ruling palaces, knots were used to signify dignity and prestige. For religious purposes knots decorated Buddhist ornaments. The most common use of knots was in Norigae, traditional Korean ornaments worn by women to decorate clothing.
The instructions on how to create a slippery eight loop is as follows: Begin by creating a figure eight knot with one end long enough to be looped through it again; Make sure that the figure eight loop is not tight, but rather quite loose with obvious gaps; Bring the long, working end to the top of the knot
Pretzel link knot – in knot theory, a branch of mathematics, a pretzel link is a special kind of link; Prusik knot – friction hitch or knot used to put a loop of cord around a rope; Portuguese bowline a.k.a. French bowline – variant of the bowline with two loops that are adjustable in size; Portuguese whipping – a type of whipping knot
A small knot. The small knot, also known as oriental knot, Kent knot, or simple knot, is the simplest method of tying a necktie. Unlike the Four-in-hand knot and Windsor knot, the small knot is not self-releasing. The small knot is tied inside out, though this can be mitigated by giving the tie a half-twist during the tying process.
The Cat's paw is a knot used for connecting a rope to an object. It is very similar to the cow hitch except there is an additional twist on each side of the bight, making it less prone to slipping. The cat's-paw is the common hook hitch for slings.
Create a loop in the rope. Then pull a bight of the working part through the loop, creating an overhand noose knot. Pull another bight of the working part through the loop of the previous stitch. Tighten the stitch to the desired degree by pulling on both sides of the loop. Adjust the loop by pulling on the working end to keep it a reasonable size.
Friction knots are held in place by the friction between the windings of line. Knotted-ends knots are held in place by the two ends of the line being knotted together. Stopping may be either a temporary whipping or seizing, the commonest variety consisting of a few round turns finished off with a reef knot .