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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.
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} star polygon ; 5 2 knot/Three-twist knot - the twist knot with three-half twists
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.
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.
Since the world lines form a mathematical braid, braid theory, a related field to knot theory, is used in studying the properties of such a computer, called a topological quantum computer. [ 6 ] A development related and complementary to knot theory is circuit topology which was originally proposed by Alireza Mashaghi, [ 7 ] as a theory that ...
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.