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?

>>5
Thank you. Though I am still not sure that x(t) = x(t + m) and y(t) = y(t + m) is enough since the curve can end up at the same point but point in a different direction.