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5 2. 1 link/ Whitehead link - two projections of the unknot: one circular loop and one figure eight-shaped loop intertwined such that they are inseparable and neither loses its form (L5a1) Brunnian link - a nontrivial link that becomes trivial if any component is removed. 6 3. 2 link/ Borromean rings - three topological circles which are linked ...
Stick number. 2,3 torus (or trefoil) knot has a stick number of six. In the mathematical theory of knots, the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed to form a knot. Specifically, given any knot , the stick number of , denoted by , is the smallest number of edges ...
In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself ( crossing switch) to untie it. If a knot has unknotting number , then there exists a diagram of the knot which can be changed to unknot by switching crossings. [1] The unknotting number of a knot is ...
Cinquefoil knot. In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. It is listed as the 51 knot in the Alexander-Briggs notation, and can also be described as the (5,2)- torus knot. The cinquefoil is the closed version ...
Bridge number was first studied in the 1950s by Horst Schubert. [2] [3] The bridge number can equivalently be defined geometrically instead of topologically . In bridge representation, a knot lies entirely in the plane apart for a finite number of bridges whose projections onto the plane are straight lines. Equivalently the bridge number is the ...
Granny knot (mathematics) and Square knot (mathematics) are a connected sum of two Trefoil knots. Perko pair, two entries in a knot table that were later shown to be identical. Stevedore knot (mathematics), a prime knot with crossing number 6. Three-twist knot is the twist knot with three-half twists, also known as the 5 2 knot.
In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to determine if the problem admits a polynomial time algorithm; that is, whether the problem lies in the ...
The three-twist knot is a hyperbolic knot, with its complement having a volume of approximately 2.82812. If the fibre of the knot in the initial image of this page were cut at the bottom right of the image, and the ends were pulled apart, it would result in a single-stranded figure-of-nine knot (not the figure-of-nine loop). Example