If you are on a desert island and have forgotten the value of pi and need it desperately, you can find it experimentally. One amusing though tedious method would require throwing a short, straight twig onto parallel lines drawn in the beach sand. You will be able to compute pi from:

pi = 2lN/dH,

where l = the length of the twig, which must be less than d, separation of the parallel lines. N = the number of throws. H = the number of times the twig crosses one of the lines.

One famous performance of this experiment was by M. Lazzarini in 1901. He reported that in 3408 throws he got 1808 intersections, leading to:

pi = 3.1415929

Actually, the final digit should be a 6. Thus, Lazzarini measured pi to a few parts in 10 million.

Recently, L. Badger, Weber State University, concluded that Lazzarini probably never actually performed his experiment. His results were just too good -- too fortuitous! If the number of hits had been 1807 or 1809, pi would have been wrong by 1 part in 2,000.

As it turns out, a Chinese mathematician of the 5th Century pointed out that 355/113 = 3.1415929. It is very suspicious that Lazzarini's 3408 = 355 x 16, and 1808 = 113 x 16. Badger thinks that Lazzarini's experiment was only a "thought" experiment based on the ratio 355/113.

(Maddox, John; "False Calculation of Pi by Experiment," Nature, 370:323, 1994.)