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epicycloid with a minor radius (R2) of 0 is a circle. This is a degenerate form.

Equations

If the rolling circle has radius , and the fixed circle has radius , then the parametric equations for the curve can be given by either:
:or:
:

This can be written in a more concise form using complex numbers as

:

where
* the angle
* the rolling circle has radius , and
* the fixed circle has radius .

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