One approach to random number generation that had always intrigued me is Kinderman and Monahan’s (1977) ratio-of-uniform method. The method is based on the result that the uniform distribution on the set A of (u,v)’s in R⁺xX such that 0≤u²≤ƒ(v/u) induces the distribution with density proportional to ƒ on V/U. Hence the name. The proof