Questions tagged [knots]

Questions about exploring knot theory using Mathematica.

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Plot a Satellite Knot

I need some help to plot a Satellite or cable knot. For example, see figure A torus knot and a cable knot. (a) The red curve lying on the yellow torus is a (2,3) torus knot. (b) The embedded yellow ...
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7 votes
4 answers
426 views

RegionPlot3D KnotData

Is it possible to find or construct a RegionPlot out of KnotData? My motivation is to Texture...
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2 votes
2 answers
213 views

Issue Installing Knot Theory

I have been trying to install the Knot Theory package from the knot atlas, but have been unsuccessful. Firstly I tried the command << KnotTheory` but ...
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0 votes
0 answers
56 views

generating torus and n-torus knots in mathematica

I am wondering if it's possible to either algorithmically generate or access a built in database of n-torus knots in Mathematica? If not, are there any known databases or algorithms which I could ...
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2 votes
1 answer
273 views

How can I reduce the error estimate of numerical integration in Mathematica?

Before introducing the integral I want to go through some definitions. Define triangles $T_1$ and $T_2$ by the points $\{a,b,c\}$ and $\{d,e,f\}$ respectively. Define $$D(u,v,x,y) = sign(\det (y-u,y-v,...
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1 vote
0 answers
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Export Basis spline information to matlab

i am new to Mathematica. I have generated the contours of this image with the following code ...
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5 votes
1 answer
204 views

Orient a Knot Diagram

I need some help to orient a diagram knot For example if I have the diagram KnotData["Trefoil,"KnotDiagram"] How can I orient the diagram? I have tried to find a ...
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2 votes
0 answers
131 views

Plotting symmetric closed loop on surface of sphere (plotting spherical knot)

Here are some my attempts. ...
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3 votes
0 answers
213 views

Alexander polynomials for Pretzel knots

All knots, such as this torus knot, KnotData[{"TorusKnot", {3, 5}}] have an associated Alexander polynomial: ...
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3 votes
2 answers
149 views

The design implication of PD[X[ #, #, #, #], X[#, #, #, #]]

In Package KnotTheory, there's a function called PD[] that takes a tabulated knot and returns its PD codes, for example: ...
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9 votes
3 answers
344 views

Issue Plotting Torus Link

I'm having an issue plotting torus links in Mathematica. What I'm trying to generate is a (2,8) torus link like the one in the picture in Wikipedia: using equations such as those outlined here. ...
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  • 183
2 votes
2 answers
363 views

Intersection between knot and plane

I have to find, with Mathematica, the intersection between the curve defined by a knot and a plane defined by three points, in 3D space. I tried to find the intersection with ...
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2 votes
2 answers
221 views

Extracting tube style from KnotData

How do I extract the tube style (including lighting, viewpoint, ...) from KnotData["Trefoil"] and apply it to a space curve, such as ...
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1 vote
1 answer
120 views

Plot a circle in 3-D with a tangle

I'd like to plot a circle with a small tangle. I tried it but it didn't work. I want to plot it like in the picture below but only in 3-D if it is possible. What i did so far ...
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1 vote
0 answers
169 views

Deform a three-dimensional knot

Mathematica has curated knot data, e.g., KnotData[{3, 1}] One can extract the three-dimensional space curve in this way: ...
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2 votes
1 answer
216 views

Color Trefoil-Knot

i need some help to plot a three colored Trefoil knot. I found on Wolfram the code ...
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  • 133
9 votes
1 answer
317 views

Coloring strands in braids

Is there an option, or simple work-around, for coloring each strand in a three-dimensional BraidImage differently? For instance, I'd like to render a braid image ...
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1 vote
1 answer
143 views

How to pre or post process KnotData "substrate"

What I'm after might be thought of as operating on the 'rope' that KnotData[] uses. Specifically, I'd like to be able to specify that the knot is to be made of a ...
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  • 614
2 votes
1 answer
312 views

Knot diagrams and knot projection diagrams

One of Mathematica's lovely curated databases is KnotData, as you can see by running: KnotData[{"PretzelKnot", {5, 2, 3}}] ...
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1 vote
1 answer
174 views

The point movement on the torus knot

I would like to ask about the point movement on the torus knot. ...
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2 votes
1 answer
381 views

How to add color to a knot

Is there a way to use a colorscheme to a KnotData image? One way is probably convert it to a parametric form and then use ...
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12 votes
2 answers
414 views

Adapting KnotDiagramData to form more visually pleasing diagram

Graphics[KnotData[{5, 1}, "KnotDiagramData"]] gives but I would like to create diagrams like this remeniscent of Celtic knot designs (which I made by adapting the ...
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