The Lazzarini approximation of Pi

The Buffon Needle experiment provides an experimental approximation of the constant . One drops a large number of needles at random (with uniform distribution) over a set of equally spaced parallel lines. If the length of the needles is smaller than the line spacing, the number of intersection between needles and lines is a random variable, whose expected value is a simple function of . So, if N is the number of needles, H is the number of intersections between the needles and the lines, d is the line spacing and l is the needle length, one can compute by the formula In 1901, Lazzarini performed the experiment, reporting an astonishingly accurate value for . The experiment is now considered as a hoax, due to the finely tuned experimental design and to doubtful reported results. The simulation used the same experimental set, showing how a biased experimental design can lead to the desired result. See: