In the mathematical 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 to its mirror image is an amphicheiral knot, also called an achiral knot. The chirality of a knot is a knot invariant. A knot's chirality can be further classified depending on whether or not it is invertible.
There are only five knot symmetry types, indicated by chirality and invertibility: fully chiral, invertible, positively amphicheiral noninvertible, negatively amphicheiral noninvertible, and fully amphicheiral invertible.[1]
^Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeff (1998), "The first 1,701,936 knots" (PDF), The Mathematical Intelligencer, 20 (4): 33–48, doi:10.1007/BF03025227, MR 1646740, S2CID 18027155, archived from the original (PDF) on 2013-12-15.
field of knot theory, a chiralknot is a knot that is not equivalent to its mirror image (when identical while reversed). An oriented knot that is equivalent...
example, the unknot and the figure-eight knot are achiral, whereas the trefoil knot is chiral. In physics, chirality may be found in the spin of a particle...
pasted to the other, the edge forms a trefoil knot. The trefoil knot is chiral, in the sense that a trefoil knot can be distinguished from its own mirror image...
equivalent of an invertible knot. There are only five knot symmetry types, indicated by chirality and invertibility: fully chiral, reversible, positively...
physical knots in order to understand knotting phenomena in DNA and other polymers. Knot theory can be used to determine if a molecule is chiral (has a...
In mathematics, in particular in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway...
strengthen the knot (see the carrick bend) or to untie a seized knot which would otherwise be difficult to release (see reef knot). Chirality is the 'handedness'...
Cable knot, see Satellite knotChiralknot is knot which is not equivalent to its mirror image. Double torus knot, a knot that can be embedded in a double...
p<q<2p} . A torus knot is trivial iff either p or q is equal to 1 or −1. Each nontrivial torus knot is prime and chiral. The (p,q) torus knot is equivalent...
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...
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....
Scoubidou (Craftlace, scoobies, lanyard, or gimp) is material used in knotting craft. It originated in France, where it became a fad in the late 1950s...
of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied...
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...
Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait...
In mathematical knot theory, 74 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism...
In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other...
boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most...
the Rosendahl Bend) is an end-to-end joining knot formed by two symmetrically interlinked overhand knots. It is stable, secure, and highly resistant to...
In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules...
bowline, Cossack knot (Russian: Казачий узел), reverse bowline, or 'anti-bowline' is in a class of knots known as 'eye knots' or 'loop knots'. The eye is...
In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is...
Global Information