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Figure-eight knot of practical knot-tying, with ends joined. In knot theory, a figure-eight knot (also called Listing's knot [1]) is the unique knot with a crossing number of four. This makes 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.
In topology, knot theory is the ... The Dowker–Thistlethwaite notation for this labelling is the sequence: 6, −12, 2, 8, −4, −10. A knot diagram has more than ...
7 1 knot, septafoil knot, (7,2)-torus knot - a prime knot with crossing number seven, which can be arranged as a {7/2} star polygon ; 7 4 knot, "endless knot" 8 18 knot, "carrick mat" 10 161 /10 162, known as the Perko pair; this was a single knot listed twice in Dale Rolfsen's knot table; the duplication was discovered by Kenneth Perko
A framed knot is the extension of a tame knot to an embedding of the solid torus D 2 × S 1 in S 3. The framing of the knot is the linking number of the image of the ribbon I × S 1 with the knot. A framed knot can be seen as the embedded ribbon and the framing is the (signed) number of twists. [8] This definition generalizes to an analogous ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
The two curves of this (2, 8)-torus link have linking number four. In mathematics, ... It is an important object of study in knot theory, algebraic topology, ...
The simplest example of a non-invertible knot is the knot 8 17 (Alexander-Briggs notation) or .2.2 (Conway notation). The pretzel knot 7, 5, 3 is non-invertible, as are all pretzel knots of the form (2 p + 1), (2 q + 1), (2 r + 1), where p , q , and r are distinct integers, which is the infinite family proven to be non-invertible by Trotter.
The figure-eight knot or figure-of-eight knot is a type of stopper knot. It is very important in both sailing and rock climbing as a method of stopping ropes from running out of retaining devices. Like the overhand knot , which will jam under strain, often requiring the rope to be cut, the figure-eight will also jam, but is usually more easily ...