Torus knots#
See also: https://katlas.org/wiki/36_Torus_Knots
Torus knot 3:2#
The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D01a_TorusKnotp3q2.3D.xml (D01a-f).
Some text
See also: https://mathworld.wolfram.com/TrefoilKnot.html
See also: https://katlas.org/wiki/T(3,2)
The example below uses the following code in C#
double R = 100;
double r = 25;
double p = 3;
double q = 2;
var x = ((R + r * Math.Cos(p * t)) * Math.Cos(q * t)) / 50;
var y = ((R + r * Math.Cos(p * t)) * Math.Sin(q * t)) / 50;
var z = (r * Math.Sin(p * t)) / 50;
\(\quad\) 
\(\quad\) 
\(\quad\) 
\(\quad\) 
Torus knot 5:2#
The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D02a_TorusKnotp5q2.3D.xml (D02a-f).
Some text
See also: https://en.wikipedia.org/wiki/Cinquefoil_knot
See also: https://katlas.org/wiki/T(5,2)
The example below uses the following code in C#
double R = 100;
double r = 25;
double p = 5;
double q = 2;
var x = ((R + r * Math.Cos(p * t)) * Math.Cos(q * t)) / 50;
var y = ((R + r * Math.Cos(p * t)) * Math.Sin(q * t)) / 50;
var z = (r * Math.Sin(p * t)) / 50;
\(\quad\) 
\(\quad\) 
\(\quad\) 
\(\quad\) 
Torus knot 7:2#
The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D03a_TorusKnotp7q2.3D.xml (D03a-f).
Some text
See also: https://en.wikipedia.org/wiki/71_knot
See also: https://katlas.org/wiki/T(7,2)
See also: https://katlas.org/wiki/7_1
The example below uses the following code in C#
double R = 100;
double r = 25;
double p = 7;
double q = 2;
var x = ((R + r * Math.Cos(p * t)) * Math.Cos(q * t)) / 50;
var y = ((R + r * Math.Cos(p * t)) * Math.Sin(q * t)) / 50;
var z = (r * Math.Sin(p * t)) / 50;
\(\quad\) 
\(\quad\) 
\(\quad\) 
\(\quad\) 
Torus knot 7:3#
The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D04a_TorusKnotp7q3.3D.xml (D04a-f).
Some text
See also: https://katlas.org/wiki/T(7,3)
The example below uses the following code in C#
double R = 100;
double r = 25;
double p = 7;
double q = 3;
var x = ((R + r * Math.Cos(p * t)) * Math.Cos(q * t)) / 50;
var y = ((R + r * Math.Cos(p * t)) * Math.Sin(q * t)) / 50;
var z = (r * Math.Sin(p * t)) / 50;
\(\quad\) 
\(\quad\) 
\(\quad\) 
\(\quad\) 
Torus knot 15:2#
The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D05a_TorusKnotp15q2.3D.xml (D05a-f).
Some text
See also: https://katlas.org/wiki/T(15,2)
The example below uses the following code in C#
double R = 100;
double r = 25;
double p = 15;
double q = 2;
var x = ((R + r * Math.Cos(p * t)) * Math.Cos(q * t)) / 50;
var y = ((R + r * Math.Cos(p * t)) * Math.Sin(q * t)) / 50;
var z = (r * Math.Sin(p * t)) / 50;
\(\quad\) 
\(\quad\) 
\(\quad\) 
\(\quad\) 