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/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.