References
D. H. Bailey, The computation of pi to 29,360,000 decimal digits using Borweins’ quartically convergent algorithm,Mathematics of Computation 42 (1988), 283–296.
D. H. Bailey, P. B. Borwein, and S. Plouffe, On the rapid computation of various polylogarithmic constants, (to appear in Mathematics of Computation). Available fromhttp://www.cecm.sfu/personal/pborwein/.
P. Beckmann,A History of Pi, New York: St. Martin’s Press (1971).
L. Berggren, J. M. Borwein, and P. B. Borwein,A Sourcebook on Pi, New York: Springer-Verlag (to appear).
J. M. Borwein and P. B. Borwein,Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, New York: Wiley (1987).
J. M. Borwein and P. B. Borwein, Ramanujan and pi,Scientific American (February 1987), 112-117.
J. M. Borwein, P. B. Borwein, and D. H. Bailey, Ramanujan, modular equations, and approximations to pi, or how to compute one billion digits of pi,American Mathematical Monthly 96 (1989), 201–219. Also available from the URLhttp://www.cecm.sfu.ca/personal/pborwein/.
R. P. Brent, Fast multiple-precision evaluation of elementary functions,Journal of the ACM 23 (1976), 242–251.
D. Chudnovsky and C. Chudnovsky, personal communication (1995).
H. R. P. Ferguson and D. H. Bailey, Analysis of PSLQ, an integer relation algorithm, unpublished, 1996.
T. L. Heath (trans.), The works of Archimedes, inGreat Books of the Western World (Robert M. Hutchins, ed.), Encyclopedia Britannica (1952), Vol. 1, pp. 447–451.
Y. Kanada, personal communication (1996). See also Kanada’s book (in Japanese),Story of Pi, Tokyo: Tokyo-Toshyo Co. Ltd. (1991).
D. E. Knuth,The Art of Computer Programming, Reading, MA: Addison-Wesley, (1981), Vol. 2.
R. Preston, The mountains of pi,The New Yorker, 2 March 1992, 36-67.
S. D. Rabinowitz and S. Wagon, A spigot algorithm for pi,American Mathematical Monthly 103 (1995), 195–203.
E. Salamin, Computation of pi using arithmetic-geometric mean,Mathematics of Computation 30 (1976), 565–570.
D. Shanks and J. W. Wrench, Calculation of pi to 100,000 decimals,Mathematics of Computation 16 (1962), 76–79.
S. Wagon, Isit normal?Mathematical Intelligencer 7 (1985), no. 3, 65–67.
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bailey, D.H., plouffe, S.M., borwein, P.B. et al. The quest for PI. The Mathematical Intelligencer 19, 50–56 (1997). https://doi.org/10.1007/BF03024340
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DOI: https://doi.org/10.1007/BF03024340