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

Hence

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