From: "Vincent R. Johns" Newsgroups: sci.math Subject: Re: pi as a probability Date: Mon, 29 Jul 1996 11:32:38 -0500 mchen@nyc.pipeline.com wrote: > > I believe the problem you are referring to is the "Buffon Needle Problem" - > it can be found in many probability books (check the index). Here are some references on WWW to Buffon's needle, including some simulations: [http://www.mste.uiuc.edu/reese/buffon/buffon.html] [http://www.stats.mu.oz.au:8001/discday/kostya/pinee.html] [http://www.eg.bucknell.edu/~kapolka/cs204/labs/needle.html] If you have a PC with graphic display, a simulation is available at [http://archives.math.utk.edu/software/msdos/probability/ jkbuffon/.html] in a file called [http://archives.math.utk.edu/ software/msdos/probability/jkbuffon/jkbuffon.zip]. It's possible to get excellent results from the needle- tossing technique, if you don't mind cheating a bit as you do it. See, for example, [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/ Pi_through_the_ages.html], which includes this: "Various people have tried to calculate pi by throwing needles. The most remarkable result was that of Lazzerini (1901), who made 34080 tosses and got pi = 355/113 = 3.1415929 which, incidentally, is the value found by Tsu Ch'ung Chi. This outcome is suspiciously good, and the game is given away by the strange number 34080 of tosses. Kendall and Moran comment that a good value can be obtained by stopping the experiment at an optimal moment. If you set in advance how many throws there are to be then this is a very inaccurate way of computing pi. Kendall and Moran comment that you would do better to cut out a large circle of wood and use a tape measure to find its circumference and diameter. "Still on the theme of phoney experiments, Gridgeman, in a paper which pours scorn on Lazzerini and others, created some amusement by using a needle of carefully chosen length k = 0.7857, throwing it twice, and hitting a line once. His estimate for pi was thus given by 2 x 0.7857 / pi = 1/2 from which he got the highly creditable value of pi = 3.1428. He was not being serious!" -- Vincent Johns