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Finding Pi


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

What would be the quickest algorithm to find pi?

I know about this one

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.


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_ 
From Scientific American, a Fireside Book published by Simon and 
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/   
    
Associated Topics:
High School Number Theory
Middle School Number Sense/About Numbers
Middle School Pi

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