epicycloid (cardioid) pedal curve

    n=1 cardioid

n=2 Nephroid

n=3 epicycloid

The pedal curve of an epicycloid

with pedal point at the origin is

For an n-cusped epicycloid with (a,b)=(n,1), the pedal curve with pedal point at the origin is

Noting that

so solving for t gives

and plugging in gives a polar equation of

which is the equation of a rose

Cardioid:

• Cardioid

• Tangent

• Osculating circle

cardioid pedal curve (rose):

• cardioid pedal curve

• Tangent

• Osculating circle

(pedal point at the center)