| Beckmann, Peter, A History of Pi , New York: St. Martin's Press, 1971.
This book lists estimates of p through history on pages 196 C197. It is a fascinating account of the history of p . Chapter 13 includes the derivation of Machin's arctangent formula. Berggren, Lennart, Jonathan Borwein, and Peter Borwein, eds. Pi: A Source Book , New York: Springer-Verlag, 1997.
This invaluable collection of writings on p ranges from technical and scholarly papers to the quirky and whimsical. Borwein, Jonathan M., and Peter B. Borwein, "Ramanujan and Pi." In Pi: A Source Book , edited by L. Berggren, J. Borwein, and P. Borwein, New York: Springer-Verlag, 1997.
This paper is about Ramanujan's formulas for p , but it also includes the Borweins' algorithm for generating billions of p 's digits. Ramanujan, "Modular Equations and Approximations to p ." In Pi: A Source Book , edited by L. Berggren, J. Borwein, and P. Borwein, New York: Springer-Verlag, 1997.
In this work, Ramanujan derives his formulas that estimate the value of p to various numbers of decimal digits. Reitwiesner, "An ENIAC Determination of p and e to 2000 Decimal Places." In Pi: A Source Book , edited by L. Berggren, J. Borwein, and P. Borwein, New York: Springer-Verlag, 1997.
Reitwiesner describes using an arctangent formula on the ENIAC to compute the first 2,035 decimal digits of p . This papter is reprinted in Berggren, Borwein, and Borwein, which includes a table of more arctangent formulas on page 687. Shanks, Daniel, and John W. Wrench, Jr., "Calculation of p to 100,000 Decimals." In Pi: A Source Book , edited by L. Berggren, J. Borwein, and P. Borwein, New York: Springer-Verlag, 1997.
Shanks and Wrench describe using an arctangent formula on the IBM 7090 to compute the first 100,200 decimal digits of p . |
