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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 ...
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.
ABoK. #1010, #1716. Instructions. [1] The bowline ( / ˈboʊlɪn / or / ˈboʊlaɪn /) [2] is an ancient and simple knot used to form a fixed loop at the end of a rope. It has the virtues of being both easy to tie and untie; most notably, it is easy to untie after being subjected to a load. The bowline is sometimes referred to as king of the ...
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 ...
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 ...
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 ...
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 ...
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 ...