Parametric Equations of a Torus

The Cartesion equation for a torus takes the form

(if any ofand z are interchanged, a similar, rotated torus will result).

We can obtain a parametric equation by settingas in the diagram below.

The Cartesian equation becomes

Square rooting both sides gives


Now recognise that for constantthis equation defines a circle around the– axis of radiusso setand

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