Read the
epicycloid writeup first.
The
nephroid is a
kidney-shaped
plane algebraic curve.
It is an epicycloid such that the outer of the two
circles in the
definition of an epicycloid has
radius twice that of the other,
a, say.
An equation for the nephroid is (x2 + y2
- 4a2)3 = 108a4y2.
Like other epicycloids it finds applications in the study of gears.