### Knot—Wolfram Language Documentation

"Knot" entity classes include common mathematical types of knots, such as "Alternating", "Chiral" and "Torus", together with the negations of these. Mathematical properties are available for most "Knot" entities that are concisely representable and either well known or straightforward to compute.

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Get price### From knot groups to knot semigroups

Knot semigroups: a new algebraic approach to knots and braids Alexei Vernitski University of Es On the picture: the logo of a shopping centre in Colchester presents what in this talk we shall treat as the generators of the semigroup of the trefoil knot

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Get price### KnotData - Wolfram Mathematica 8 Documentation

KnotData[knot, " property"] gives the specified property for a knot.KnotData[knot] gives an image of the knot.KnotData["class"] gives a list of knots in the specified class.

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Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. ... trefoil knot. Specify a knot using Alexander–Briggs notation: 8_1 knot. Compare several knots: Stevedore knot, figure eight knot ... Wolfram for Education; MathWorld; This website uses ...

Get price### Explore Torus Knots: New in Wolfram Language 12

In addition to the standard tabulated knots up to 10 crossings, the "Knot" domain also contains additional entities corresponding to some parametrized families of knots, the most notable being torus knots.. A torus knot can be visualized as the knot obtained by looping a string through the hole of a torus times with revolutions before joining its ends, when and are relatively prime positive ...

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Comprehensive list of Wolfram|Alpha's computable data topics. Built from the extensive Wolfram Knowledgebase repository. Wide breadth of coverage from science & technology to society & culture.

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Wolfram Language Revolutionary knowledge-based programming language. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Wolfram Science Technology-enabling science of the computational universe.

Get price### Computer Aided Knot Theory Using ... - Wolfram Research

We introduce a computer tool called Knot2000(K2K) which was developed for the purpose of support for the research of knot theory. K2K is a package on Mathematica in which consists of 19 functions and it has already been opened to the public with other external programs and data files. In this paper, we will describe focusing on the usages of each functions and some examples of effective ways ...

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Get price### Trefoil knot - Wikipedia

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 together the two loose ends of a common overhand knot, resulting in a knotted loop.As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.

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Wolfram Community forum discussion about [GIF] BCC (Minimal figure-eight knot on the body-centered cubic lattice). Stay on top of important topics and build connections by joining Wolfram Community groups relevant to your interests.

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Keywords: density plot, non-linear inequality, polynomial vector field, world map, iterated transcendental function, three-dimensional bar chart, stellated icosahedron, Scherk minimal surface, strange attractor, Enneper surfaces, conchoid surfaces, trinoid minimal surfaces, trefoil knot, figure-eight knot, torus knot, symmetric quasitilings, color models, lighting models, graphics gallery

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Get price### Decorative Knotting Using Trigonometric Parametrizations.

The Trefoil Knot, when considered as a simple outward facing loop pattern (), requires separate handling and will be considered first. It can be described by the following equations: Figure 3 shows a Trefoil Knot ( and demonstrates the effect of varying the ratio in Equations 1. When (in this case 0.5) a .

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[Submitted on 11 Mar 1998] Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity. D. J. Broadhurst. In each of the 10 cases with propagators of unit or zero mass, the finite part of the scalar 3-loop tetrahedral vacuum diagram is reduced to 4-letter words in the 7-letter alphabet of the 1-forms Ω:=dz/z and ωp:=dz/(λ−p−z), where λ is the ...

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Feb 15, 2015· In-text: (Inoue, 2015) Your Bibliography: Inoue, A., 2015. On colorability of knots by rotations, torus knot and PL trochoid. Topology and its Applications, 183, pp ...

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It is based on a trefoil knot tessellated with different coloured tiles. In mathematics the trefoil knot is the simplest non-trivial knot. In drug discovery, the trefoil knot fold is a structure found in proteins where it is part of the active site or a ligand-binding site and is critical to .

Get price### Knot Theory on Sage – Christopher Duston's Home

Aug 01, 2017· First, we should make sure we can use the tools on Sage to reproduce known results, so I'll do that with the most popular non-trivial knot, the trefoil (it also happens the trefoil is a (2,3) torus knot, and I'm going to be interested in torus knots in general).

Get price### Trefoil knot - Infogalactic: the planetary knowledge core

In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot.The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop.As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.. The trefoil knot is named after the three-leaf clover (or trefoil) plant.

Get price### Visualize the TNB Basis of a Knot - Wolfram Research

Visualize the TNB Basis of a Knot . FrenetSerretSystem will compute the orthonormal basis associated to a curve in any dimension. In three dimensions, this basis is usually called the Tangent/Normal/Binormal or TNB basis.

Get price### Visualize the TNB Basis of a Knot - Wolfram Research

Visualize the TNB Basis of a Knot . FrenetSerretSystem will compute the orthonormal basis associated to a curve in any dimension. In three dimensions, this basis is usually called the Tangent/Normal/Binormal or TNB basis.

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Orientation change of a Dirac string and Net field calculation using knot generators. Theorem- The knot group of k is generated by the elements subject to relations . The trefoil knot –we have three generators on eliminating we get (2.2)- Then the group is defined as(2.2)- A to (12), b to(23) ↕HOMOMORPHISM From G to symmetric group on ...

Get price### KnotData—Wolfram Language Documentation

KnotData[knot, " property"] gives the specified property for a knot. KnotData[knot] gives an image of the knot. KnotData["class"] gives a list of knots in the specified class.

Get price### It's Knot an Unknot (or Not?)

Apr 25, 2016· With the 2-dimensional knot inside of the torus. The whole thing, or knot K3, is called a satellite knot, and the knot K2 is called the companion knot of the satellite. You can think of it, maybe, as knot where the the satellite knot, or the final knot, orbits around (or is inside) the companion torus knot that is the center of the knot as a whole.

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Wolfram Language Revolutionary knowledge-based programming language. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Wolfram Science Technology-enabling science of the computational universe.

Get price### Space-curves & Generalized Knots in ... - Wolfram Research

Knots, braids, bends, links, hitches, weaves etc. are described by d-dimensional space-curves. Their projections can be shown as 2D shadows, 2.5D knot diagrams, and 3D tubes using piece-wise cubic interpolation. Mathematical knots and links are closed 3D lines that cannot be untangled without passing lines through lines. Braids provide compact knot descriptors; bends join two ropes; hitches ...

Get price### 3D Printing the Trefoil Knot and its Pages — Fred Hohman

May 08, 2015· Fred Hohman CV Publications Everything Else 3D Printing the Trefoil Knot and its Pages May 8, 2015. At the University of Georgia I spent three semesters exploring 3D printing techniques in topology under Dr. David Gay in the Mathematics Department, in particular, visualizing complex shapes and knots using a MakerBot Replicator 2.. My first designed, 3D printed trefoil knot.

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3D Squared Trefoil

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The trefoil knot is the simplest example of a nontrivial knot. This Demonstration shows the projection of a two-parameter version of the trefoil knot and plots the minimum (in blue) and maximum (in red) curvature points along the knot.

Get priceThe trefoil knot is the simplest example of a nontrivial knot. This Demonstration shows the projection of a two-parameter version of the trefoil knot and plots the minimum (in blue) and maximum (in red) curvature points along the knot.

Get priceDie Orthonormalbasis eines Knotens visualisieren . FrenetSerretSystem berechnet die Orthonormalbasis (ONB) einer Kurve in jeder beliebigen Dimension. Im dreidimensionalen Raum nennt man diese Basis das begleitende Dreibein. Schlagen Sie die Funktion f ü r den Knoten nach.

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