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Finding Pi

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Date: 11/14/97 at 16:35:12
From: Kelly Trinh
Subject: Finding pi

What would be the quickest algorithm to find pi?

pi /4 = 1 - 1/3 + 1/5 - 1/7 + ....

however this one converges *SO* slow its not funny. Even on a p166 it
takes a lot of iterations to get pi to ten decimal places.
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Date: 11/23/97 at 18:27:21
From: Doctor Bill
Subject: Re: Finding pi

Dear Kelly,

There probably isn't any "quickest" algorithm for finding pi, but
there are many and varied ones.  Another one you might try is;

pi/2 = 2/1 x 2/3 x 4/3 x 4/5 x 6/5 x 6/7 x 8/7 x 8/9 ...

This is one of the simplest (can you see the pattern that is
developing between the odd and even numbers in the numerators and
denominators?) and was discovered by John Wallis (1616-1703).

There is a book published by St. Martin's Press called _A History of
Pi_ by Petr Beckmann that has much about pi and the attempts to
calculate it. Also, In Martin Gardner's _New Mathematical Diversions_
Schuster, he has a very interesting chapter on pi and some of its
history.

-Doctor Bill,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Number Theory