consider: a square, of side r, with an arc drawn from (r,0) to (0,r) around (0,0). As - Area of square Aa - Area inside of arc Ds - "darts" falling in square (total darts) Da - "darts" falling in arc (somewhat less than Ds) k - a constant: relating to the density of "darts" distributed uniformly (we suppose) throughout the area Ds. Pi - the irrational number 2 2 (Pi)kr Ds = kr Da = ------ 4 Da Pi Da -- = -- ... 4 -- = Pi Ds 4 Ds The number of darts falling within r of the origin is noted in Da, the total number of darts fallen is noted in Ds. The ratio is assumed to approach Pi as Ds approaches infinity (oo).