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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 ").
The term knot is also applied to embeddings of S j in S n, especially in the case j = n − 2. The branch of mathematics that studies knots is known as knot theory and has many relations to graph theory.
A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory. Implicit in this definition is that there is a trivial reference link, usually called the unlink, but the word is also sometimes used in context where there is no notion of a trivial link.
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 ...
Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R 3.
Trefoil knot without 3-fold symmetry being unknotted by one crossing switch. Whitehead link being unknotted by undoing one crossing. 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.
Figure-eight knot of practical knot-tying, with ends joined. In knot theory, a figure-eight knot (also called Listing's knot [1]) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure-eight knot is a prime knot.
This is a list of mathematical theories. Almgren–Pitts min-max theory; Approximation theory; ... Knot theory; L-theory; Lattice theory; Lie theory; M-theory ...