.. |newpage| raw:: latex

   \newpage



.. |br| raw:: html

   <br />






|newpage|

Torus knots
==============================================================

See also: https://katlas.org/wiki/36_Torus_Knots



Torus knot 3:2
--------------------------------------------


Some text

See also: https://mathworld.wolfram.com/TrefoilKnot.html

See also: https://katlas.org/wiki/T(3,2)


An example in C\#

.. code-block:: csharp

    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;




|Path_Torus_Knot_3_2_aa| `\quad` |Path_Torus_Knot_3_2_bb| `\quad` |Path_Torus_Knot_3_2_cc|

.. |Path_Torus_Knot_3_2_aa| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_3_2_aa.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_3_2_bb| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_3_2_bb.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_3_2_cc| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_3_2_cc.3D.xml.jpg
   :width: 30 %




**Left figure**: Torus knot 3:2 (see also  Wikipedia :cite:p:`Wikipedia2D010`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Middle figure**: Torus knot 3:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Right figure**: Torus knot 3:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.





|newpage|

Torus knot 5:2
-------------------------------------------


Some text

See also: https://en.wikipedia.org/wiki/Cinquefoil_knot

See also: https://katlas.org/wiki/T(5,2)



An example in C\#

.. code-block:: csharp

    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;



|Path_Torus_Knot_5_2_aa| `\quad` |Path_Torus_Knot_5_2_bb| `\quad` |Path_Torus_Knot_5_2_cc|

.. |Path_Torus_Knot_5_2_aa| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_5_2_aa.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_5_2_bb| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_5_2_bb.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_5_2_cc| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_5_2_cc.3D.xml.jpg
   :width: 30 %




**Left figure**: Torus knot 5:2 (see also  Wikipedia :cite:p:`Wikipedia2D010`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Middle figure**: Torus knot 5:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Right figure**: Torus knot 5:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.




|newpage|

Torus knot 7:2
----------------------------------------


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




An example in C\#

.. code-block:: csharp

    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;




|Path_Torus_Knot_7_2_aa| `\quad` |Path_Torus_Knot_7_2_bb| `\quad` |Path_Torus_Knot_7_2_cc|

.. |Path_Torus_Knot_7_2_aa| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_7_2_aa.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_7_2_bb| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_7_2_bb.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_7_2_cc| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_7_2_cc.3D.xml.jpg
   :width: 30 %




**Left figure**: Torus knot 7:2 (see also  Wikipedia :cite:p:`Wikipedia2D010`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Middle figure**: Torus knot 7:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Right figure**: Torus knot 7:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.




|newpage|

Torus knot 7:3
--------------------------------------


Some text

See also: https://katlas.org/wiki/T(7,3)



An example in C\#

.. code-block:: csharp

    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;



|Path_Torus_Knot_7_3_aa| `\quad` |Path_Torus_Knot_7_3_bb| `\quad` |Path_Torus_Knot_7_3_cc|

.. |Path_Torus_Knot_7_3_aa| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_7_3_aa.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_7_3_bb| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_7_3_bb.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_7_3_cc| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_7_3_cc.3D.xml.jpg
   :width: 30 %




**Left figure**: Torus knot 7:3 (see also  Wikipedia :cite:p:`Wikipedia2D010`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Middle figure**: Torus knot 7:3 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Right figure**: Torus knot 7:3 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.




|newpage|

Torus knot 15:2
------------------------------------------


Some text

See also: https://katlas.org/wiki/T(15,2)



An example in C\#

.. code-block:: csharp

    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;


|Path_Torus_Knot_15_2_aa| `\quad` |Path_Torus_Knot_15_2_bb| `\quad` |Path_Torus_Knot_15_2_cc|

.. |Path_Torus_Knot_15_2_aa| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_15_2_aa.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_15_2_bb| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_15_2_bb.3D.xml.jpg
   :width: 30 %

.. |Path_Torus_Knot_15_2_cc| image:: ../_static/PathSurfaces/TorusKnots/Path_Torus_Knot_15_2_cc.3D.xml.jpg
   :width: 30 %




**Left figure**: Torus knot 15:2 (see also  Wikipedia :cite:p:`Wikipedia2D010`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Middle figure**: Torus knot 15:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.

**Right figure**: Torus knot 15:2 (see also  Wikipedia :cite:p:`Wikipedia2D011`, :cite:t:`Gray2006`,  :cite:t:`Krivoshapko2015`). Camera angles are `\theta=135^\circ` and `\phi = -12^\circ`.