Lissajous curves

That is, this form of parametric equation.

x = A sin(a t + d)
y = B sin(b t)

Why does a/b have to be rational for the curve to be closed?

So that there is some multiple of a and some multiple of b that makes them at equal angles.

Like, if one was irrational, and one wasn't, then you couldn't find a t that would make them line up

That's my guess anyways.  lol idk I'm in biochemistry and shit