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To gain further insight, mathematicians have generalized the knot concept in several ways. Knots can be considered in other three-dimensional spaces and objects other than circles can be used; see knot (mathematics). For example, a higher-dimensional knot is an n-dimensional sphere embedded in (n+2)-dimensional Euclidean space.
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 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 ...
Pretzel bread in the shape of a 7 4 pretzel knot. 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.
Two classes of knots: torus knots and pretzel knots; Cinquefoil knot also known as a (5, 2) torus knot. 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.
Knot (mathematics) Link (knot theory) Wild knots; Examples of knots Unknot; Trefoil knot; Figure-eight knot (mathematics) Borromean rings; Types of knots
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum. The prime knots with ten or fewer crossings are listed here for quick comparison of their properties and varied naming schemes.
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.