Knots - Maple Help

Examples of Knots

The following example worksheet shows various examples of knots visualized using the plots:-tubeplot and algcurves:-plot_knot commands.

Unknot

The unknot can be defined by the following parametric equations:

The Trefoil Knot

The trefoil knot can be defined by the following parametric equations:

The Figure-Eight Knot

The figure-eight can be defined by the following parametric equations:

The Lissajous Knot

The Lissajous knot can be defined by the following parametric equations:

Where , , and are integers and the phase shifts , , and are any real numbers.

The 8 21 knot (, , and ) appears as follows:

Star Knot

A star knot can be defined by using the following polynomial:

 > f := -x^5+y^2;

 (1)

Two different projections of the same polynomial

By switching x and y, different visualizations can be generated:

 > g:=(y^3-x^7)*(y^2-x^5)+y^3;

 (2)

More examples

 > f:=(y^3-x^7)*(y^2-x^5);

 (3)

 > h:=(y^3-x^7)*(y^3-x^7+100*x^13)*(y^3-x^7-100*x^13);

 (4)