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The figure eight knot complement is a double-cover of the Gieseking manifold, which has the smallest volume among non-compact hyperbolic 3-manifolds. The figure-eight knot and the (−2,3,7) pretzel knot are the only two hyperbolic knots known to have more than 6 exceptional surgeries, Dehn surgeries resulting in a non-hyperbolic 3-manifold ...
3 1 knot/Trefoil knot - (2,3)-torus knot, the two loose ends of a common overhand knot joined together 4 1 knot/ Figure-eight knot (mathematics) - a prime knot with a crossing number four 5 1 knot/ Cinquefoil knot , (5,2)-torus knot, Solomon's seal knot, pentafoil knot - a prime knot with crossing number five which can be arranged as a {5/2 ...
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 ...
The simplest knot, called the unknot or trivial knot, is a round circle embedded in R 3. [4] In the ordinary sense of the word, the unknot is not "knotted" at all. The simplest nontrivial knots are the trefoil knot (3 1 in the table), the figure-eight knot (4 1) and the cinquefoil knot (5 1). [5] Several knots, linked or tangled together, are ...
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 ...
Figure 8, a two-lobed Lissajous curve; Figure 8, in topology, the rose with two petals; Figure 8, shape described by an analemma, a curve in astronomy; Figure-eight knot (mathematics), in knot theory; Lemniscate, various types of mathematical curve that resembles a figure 8
The notion of a knot has further generalisations in mathematics, see: Knot (mathematics), isotopy classification of embeddings. Every knot in the n -sphere S n {\displaystyle \mathbb {S} ^{n}} is the link of a real-algebraic set with isolated singularity in R n + 1 {\displaystyle \mathbb {R} ^{n+1}} ( Akbulut & King 1981 ).
Figure-eight knot is fibered.. In knot theory, a branch of mathematics, a knot or link in the 3-dimensional sphere is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1-parameter family of Seifert surfaces for , where the parameter runs through the points of the unit circle, such that if is not equal to then the intersection of and is exactly .