Hypocycloid

The path of a point on a circle rolling inside a larger fixed circle. When q, the ratio of the radii, is a fraction n/d in lowest terms, the curve has n cusps and the shape of the star polygon {n/d}. Three cusps make the deltoid and four the astroid. With q = 2 the point moves on a straight line, a motion Nasir al-Din al-Tusi described in the thirteenth century.

x = (R - r) cos θ + r cos((R - r)θ/r), y = (R - r) sin θ - r sin((R - r)θ/r)

On mathcurve.com as Hypocycloïde