Who first proposed using $x^2+y^2 < 1$ Monte Carlo algorithm to calculate Pi? I'm sure everybody knows of Buffon's needle experiment in the 18th century, that is one of the first probabilistic algorithms to calculate $\pi$.

The implementation of the algorithm in computers usually calls for the use of $\pi$, or a trigonometric function, which, even if they are implemented as truncated series, sort of defeats the purpose.

To circumvent this issue, there is the well-known rejection-method algorithm: draw coordinates in the unit square, and see whether they belong to the unit quarter circle. This consists in drawing two uniform reals $x$ and $y$ in (0,1), and counting them only if $x^2+y^2 &lt; 1$. In the end, the number of coordinates that have been kept divided by the total number of coordinates is an approximation of $\pi$.

This second algorithm is usually passed off as Buffon's needle, thought it is considerably different. Unfortunately, I have not been able to track down who originated it. Does anybody have any information (documented, or at worst undocumented) as to who/when this idea originated?
The Monte-Carlo method is usually attributed to Metropolis and Ulam, the latter was a mathematician on the Manhattan project.

If my memory is good, Ulam published a paper where he computes pi using the algorithm.