for its similarity to a kidney. It was

first studied by the tireless

Huygens with additional work by

astronomer R.A. Proctor. Its

perimeter is 24 times the radius;

while its area is 12 pi times the

radius squared. For gardeners, the

five-cusped epicycloid is known as a

ranunculoid - it has a perimeter of

48 times the radius and an area of 42

pi times the radius squared. Note

that Freeth's nephroid is actually a

strophoid.