Toroidal Helices

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This Demonstration shows some examples of wrapping a tubular helix around a torus.

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You can wrap up to five equally spaced, differently colored helices. Each helix can have up to five complete revolutions (or windings) around the torus, winding right or left.

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Contributed by: Erik Mahieu (December 2014)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The parametric equations of the helix are

,

,

,

where is the radius of the ring and is the radius of the helix.

The parametric equations of the helix are

,

,

,

where is the number of helices, is the number of windings per helix, and is the winding direction ( for right and for left).



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