The pedal curve for an -cusped hypocycloid
(1)
| |||
(2)
|
with pedal point at the origin is the curve
(3)
| |||
(4)
|
Noting that
(5)
| |||
(6)
|
so solving for gives
(7)
|
and plugging in gives a polar equation of
(8)
|
which is the equation of a rose curve. In particular, the special cases and give a trifolium and quadrifolium, respectively.