I recently read about computing π using a Monte Carlo simulation in a MIT Course, and I thought that π is in no way related to randomness, absolutely it is related to the Pythagorean Theorem, for sure.
Instead of generate random points (as these random points are equally probable in a frequency bin) you could just compute a grid, and see if the point is inside the circle, if you need more precision you can increase the grid resolution.
What's the point of using Monte Carlo to compute π? It's a kind of joke? Interesting fact? Or it is just an illustration?