I am trying to write an algorithm that generates two random numbers $x_1$ and $x_2$ in a given range such that their ratio $x_1/x_2$ is an irrational number. I understand that all numbers stored on a computer are rational, so one cannot have a truly irrational number in a simulation. So, is there a way to simulate a situation where the ratio simply has a very long repeat period? How would such an algorithm look like (e.g., in Matlab)?
Any explanation would be greatly appreciated.
P.S. I am trying to simulate a physical situation where the ratio of the periods of two light waves is not rational (or rather, it has a very long repeat period), so that their combination would not appear to be periodic.