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In mathematics, a knot is an embedding of the circle (S 1) into three-dimensional Euclidean space, R 3 (also known as E 3). Often two knots are considered equivalent if they are ambient isotopic , that is, if there exists a continuous deformation of R 3 which takes one knot to the other.
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 ").
0 1 knot/Unknot - a simple un-knotted closed loop; 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
Figure-eight knot (mathematics) the only 4-crossing knot; Granny knot (mathematics) and Square knot (mathematics) are a connected sum of two Trefoil knots; Perko pair, two entries in a knot table that were later shown to be identical. Stevedore knot (mathematics), a prime knot with crossing number 6; Three-twist knot is the twist knot with ...
In knot theory, prime knots are those ... List of knots; List of mathematical knots and links; Knot tabulation (−2,3,7) pretzel knot; Notes External links. The ...
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.
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.
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.