Approximating π by throwing darts


We can approximate π using nothing more than random numbers and some simple geometry: we randomly throw darts at a square board of side r; within the square we inscribe a quadrant of a circle of radius r with its centre at (0, 0). We count all of the 'throws'; if a dart lands within the quadrant, we also count a 'hit'.

For a large number of throws, we see that:

hits throws = area-of-quadrant area-of-square

Some half-remembered geometry tells us that:

area-of-quadrant area-of-square = πr2/4 r2 = π 4


π = 4 ( area-of-quadrant area-of-square ) = 4 ( hits throws )

I first solved this problem as an undergraduate sometime in 1994 as part of a Computational Physics module. Using FORTRAN 77.