epicycloid (Nephroid) pedal curve

    n=1cardioid

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

Nephroid:

• Nephroid

• Tangent

• Osculating circle

Nephroid pedal curve (rose):

• Nephroid pedal curve

• Tangent

• Osculating circle

(pedal point at the center)