Cusps of Hypocycloid from Irrational Ratio of Circle Radii

Theorem
Consider the hypocycloid $H$ generated by a epicycle $C_1$ of radius $b$ rolling within a deferent $C_2$ of (larger) radius $a$.

Let $k = \dfrac a b$ be an irrational number.

Then $H$ has an infinite number of cusps, which are evenly and densely distributed around the circumference of $C_2$.