How to get a torus knot
If we want to get a torus knot of type (3,k), we can take three line segments drawn on a cylinder and roll up the cylinder to for a "doughnut" after having imparted a twist of a particular angle (k times 120°). We get, for example, three untied circumpherences if we try to reproduce in this way the torus knot (3,0)(we give no twist); if we give a complete twist, we obtain the torus knot (3,3).
See also the interactive animation Two numbers for a knot.
immagine di Gian Marco Todesco