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Diagram showing the (theoretical) 3:1 mechanical advantage of the Trucker's Hitch. In tightening the trucker's hitch, tension can be effectively increased by repeatedly pulling sideways while preventing the tail end from slipping through the loop, and then cinching the knot tighter as the sideways force is released. This is called "sweating a ...
Algebraic link diagram for the Borromean rings. The vertical dotted black midline is a Conway sphere separating the diagram into 2-tangles. In knot theory, the Borromean rings are a simple example of a Brunnian link, a link that cannot be separated but that falls apart into separate unknotted loops as soon as any one of its components is ...
Knot theory. In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot").
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 trefoil knot is named after the ...
A Young diagram or Young tableau, also called Ferrers diagram, is a finite collection of boxes, or cells, arranged in left-justified rows, with the row sizes weakly decreasing (each row has the same or shorter length than its predecessor). Young diagram. Listing the number of boxes in each row gives a partition of a positive integer n, the ...
Instructions. [1] Three knots often referred to as "true lover's knot", tied into a single line forming a loop. 1: also known as a Dutch bend; 2: also known as Matthew Walker knot; 3: also known as fisherman's knot /loop. The term true lover's knot, also called true love knot or simply love-knot amongst others, is used for many distinct knots.
The Borromean rings, a link with three components each equivalent to the unknot. In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory.
A knot diagram with crossings labelled for a Dowker sequence. In the mathematical field of knot theory, the Dowker–Thistlethwaite (DT) notation or code, for a knot is a sequence of even integers. The notation is named after Clifford Hugh Dowker and Morwen Thistlethwaite, who refined a notation originally due to Peter Guthrie Tait.