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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 ...
A Seifert surface bounded by a set of Borromean rings. In mathematics, a Seifert surface (named after German mathematician Herbert Seifert [1] [2]) is an orientable surface whose boundary is a given knot or link . Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most easily ...
The Oxford Companion to Ships and the Sea, Peter Kemp ed., 1976 pp 192–193. ISBN 0-586-08308-1; External links. Chip Log pattern on the webpage of the Navy & Marine Living History Association, Inc. Note: the distance given in the materials list for this pattern is 33 + 1 ⁄ 3 feet, but part C of "Construction" uses the modern distance of 47 + 1 ⁄ 4 feet.
Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q are not coprime (in which case the number of components is gcd ( p, q )). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as ...
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 ...
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Writhe of link diagrams. In knot theory, the writhe is a property of an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings. A direction is assigned to the link at a point in each component and this direction is followed all the way around each component.
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 ...