This is an instance of the general problem of finding a function F such that the distribution F(Uniform Distribution Over a [0,1]^n) has properties you desire (

This is an instance of the general problem of finding a function F such that the distribution F(Uniform Distribution Over a [0,1]^n) has properties you desire (in this case, n=2 and F is the polar transform). I have very often found myself wishing for an extensive reference table of such F functions when coding, as in: - draw one or many samples from the language's PRNG - apply F to it - get a random number that "does what I want" Unfortunately: 1. The math for F, while not hard in theory, rarely yields closed form solutions (you've got to, IIRC, find Distro^-1 and integrate it, or something like that, neither steps being easy for some distros). 2. There are very interesting "methods" to produce a similar results (such as the box-müller transform [1]), even if they involve rejection sampling. What I've never seen though is an overall theoretical + practical treatment of the problem: how do I get the distribution I want by applying a function or maybe an algorithm to the output of a uniform PRNG). If anyone is aware of such work, would love to learn about it. Keenan Crane's solution is really neat in that regard, btw. [1] https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform