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Examples of different knots including the trivial knot (top left) and the trefoil knot (below it) A knot diagram of the trefoil knot, the simplest non-trivial knot. In topology, knot theory is the study of mathematical knots.
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; 12n242/(−2,3,7) pretzel knot (p, q)-torus knot - a special kind of knot that lies on the surface of an unknotted torus in R 3
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 polygonal knot is a knot whose image in R 3 is the union of a finite set of line segments. [6] A tame knot is any knot equivalent to a polygonal knot. [6] [Note 2] Knots which are not tame are called wild, [7] and can have pathological behavior. [7] In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for ...
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.
The reef knot can capsize if one of its standing ends is pulled.. A knot that has capsized or spilled has deformed into a different structure. Although capsizing is sometimes the result of incorrect tying or misuse, it can also be done purposefully in certain cases to strengthen the knot (see the carrick bend [4]) or to untie a seized knot which would otherwise be difficult to release (see ...
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.
Knot board [] on Elbe 1 (ship, 1965). A knot is an intentional complication in cordage [1] which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bends, loop knots, and splices: a hitch fastens a rope to another object; a bend fastens two ends of a rope to each another; a loop knot is any knot creating a loop; and splice denotes any multi ...
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