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?

>>6


x(t) = x(t+m) for all t, that's how it's closed. This isn't a specific point.

At least I'm pretty certain it being closed <=> it is periodic