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