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Ramanujan, Modular Equations, and Approximations to Pi, or, How to Compute One Billion Digits of Pi

by David Bailey, Jonathan M. Borwein and Peter Borwein

Award: Merten Hasse

Year of Award: 1993, and also the Chauvenet Prize in 1993

Publication Information: The American Mathematics Monthly, Vol. 96 (1989), pp. 201-219.

Summary: A discussion of Ramanujan’s approach to approximating pi from a modern computational context.

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About the Authors: David Bailey received his B.S. in mathematics from Brigham Young University in 1972 and Ph.D. from Stanford University in 1976. He has worked for the Department of Defense in Washington, DC, and for SRI International before joining the staff of the NAS Applied Research Branch at NASA Ames Research Center. 

Jonathan M. Borwein received his B.A. in 1971 from the University of Western Ontario and his M.Sc. in 1972 and DPhil in 1974 from Oxford University where he was a Rhodes Scholar. He is currently a member of the faculty of the Department of Combinatorics and Optimization at the University of Waterloo. He is coauthor of several books, including A Dictionary of Real Numbers, written with his brother, P.B. Borwein.

Peter Borwein received his B.Sc. in 1974 from the University of Western Ontario, his M.Sc. in 1976 and his Ph.D. in 1979 from the University of British Columbia, followed by a post doctorate at Oxford and is currently at Simon Fraser University.  He was the recipient of the Chauvenet Prize in 1993 and the Ford Award in 2002.


Subject classification(s): Numerical Analysis | Calculus | Single Variable Calculus | Series
Publication Date: 
Monday, July 28, 2008