An

torus path is a curve on the surface of a torus that winds

times around the hole and

times through the hole. In this Demonstration you can vary the radius

(thickness) of the torus and the values of

and

. To help understand the numbers

and

, you can show the extra elements "around", being a circle around the hole, and "through", being a circle through the hole. The number

is the number of times the curve intersects the "through" circle, and the number

is the number of times the curve intersects the "around" circle. The torus path can be thickened to a tube with radius

.

A (2, 3) torus path forms a trefoil knot, and a (2, 5) torus path forms a surgeon's knot.