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WOLFRAM|DEMONSTRATIONS PROJECT

Torus Paths

An
(n,k)
torus path is a curve on the surface of a torus that winds
n
times around the hole and
k
times through the hole. In this Demonstration you can vary the radius
R
(thickness) of the torus and the values of
n
and
k
. To help understand the numbers
n
and
k
, you can show the extra elements "around", being a circle around the hole, and "through", being a circle through the hole. The number
n
is the number of times the curve intersects the "through" circle, and the number
k
is the number of times the curve intersects the "around" circle. The torus path can be thickened to a tube with radius
r
.
You can also show
p
equally spaced points on the torus path, and shift the points along the path. These points can be connected by lines and tubes.
A (2, 3) torus path forms a trefoil knot, and a (2, 5) torus path forms a surgeon's knot.
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