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,...

mathematics that studies knots is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional...

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...

mathematics known as knot theory. Knots and knotting have been used and studied throughout history. For example, Chinese knotting is a decorative handicraft...

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...

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies...

significant stimulus in knot theory would arrive later with Sir William Thomson (Lord Kelvin) and his vortex theory of the atom. Different knots are better at different...

mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence...

of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. The...

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...

knot is one of the most fundamental knots, and it forms the basis of many others, including the simple noose, overhand loop, angler's loop, reef knot...

In the mathematical theory of knots, a knot is tame if it can be "thickened", that is, if there exists an extension to an embedding of the solid torus...

automorphic sets). A detailed overview of racks and their applications in knot theory may be found in the paper by Colin Rourke and Roger Fenn. A rack may...

mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant. By way...

of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or...

Look up knot in Wiktionary, the free dictionary. A knot is a fastening in rope or interwoven lines. Knot or knots may also refer to: Knot (unit), of speed...

The figure-eight knot or figure-of-eight knot is a type of stopper knot. It is very important in both sailing and rock climbing as a method of stopping...

In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway...

Mathematics determining that the Conway knot is not a smoothly slice knot, answering an unsolved problem in knot theory first proposed over fifty years prior...

In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the...

Physical knot theory is the study of mathematical models of knotting phenomena, often motivated by considerations from biology, chemistry, and physics...

Knot (mathematics) Link (knot theory) Wild knots Examples of knots Unknot Trefoil knot Figure-eight knot (mathematics) Borromean rings Types of knots...

knots. Applying chemical topology and knot theory to molecular knots allows biologists to better understand the structures and synthesis of knotted organic...

dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part...

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot...

conjecture may refer to: Milnor conjecture (K-theory) in algebraic K-theory Milnor conjecture (knot theory) in knot theory Milnor conjecture (Ricci curvature) concerning...

duality. Knot theory is the study of mathematical knots. While inspired by knots that appear in daily life in shoelaces and rope, a mathematician's knot differs...

field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed). An oriented knot that is equivalent...

the "Ballantine rings". The first work of knot theory to include the Borromean rings was a catalog of knots and links compiled in 1876 by Peter Tait....

commonly used terms related to knots. Contents:  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A bend is a knot used to join two lengths of rope...