knot theory
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Knot theory — A three dimensional depiction of a thickened trefoil knot, the simplest non trivial knot … Wikipedia
knot theory — ▪ mathematics in mathematics, the study of closed curves in three dimensions, and their possible deformations without one part cutting through another. Knots may be regarded as formed by interlacing and looping a piece of string in any… … Universalium
knot theory — noun Date: 1981 a branch of topology concerned with the properties and classification of mathematical knots • knot theorist noun … New Collegiate Dictionary
List of knot theory topics — 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 together so that it cannot be undone. In precise mathematical… … Wikipedia
History of knot theory — For thousands of years, knots have been used for basic purposes such as recording information, fastening and tying objects together. Over time people realized that different knots were better at different tasks, such as climbing or sailing. Knots … Wikipedia
Crossing number (knot theory) — In the mathematical area of knot theory, the crossing number of a knot is the minimal number of crossings of any diagram of the knot. It is a knot invariant. By way of example, the unknot has crossing number zero, the trefoil knot three and the… … Wikipedia
Mutation (knot theory) — The Kinoshita–Terasaka knot and the Conway knot respectively, and how they are related by mutation. In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the… … Wikipedia
Physical knot theory — is the study of mathematical models of knotting phenomena, often motivated by physical considerations from biology, chemistry, and physics. Traditional knot theory models a knot as a simple closed loop in three dimensional space. Such a knot has… … Wikipedia
Conway notation (knot theory) — Left: A tangle a and its reflection a. Top right: Tangle addition, denoted by a + b. Center right: Tangle product, denoted by a b, equivalent to a + b. Bottom right: Ramification, denoted by a , b, equivalent to a + b In knot theory, Conway… … Wikipedia
Link (knot theory) — In mathematics, 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 … Wikipedia
