Abstract
The following comparison of the previous calculations of π performed on electronic computers shows the rapid increase in computational speeds which has taken place.
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Reference
G. Reitwiesner, “An ENIAC determination of r and e to more than 2000 decimal places,” MTAC, v. 4, 1950, p. 11–15.
S. C. Nicholson & J. Jeenel, “Some comments on a NORC computation of jr, ” MTAC, v. 9, 1955, p. 162–164.
G. E. Felton, “Electronic computers and mathematicians,” Abbreviated Proceedings of the Oxford Mathematical Conference for Schoolteachers and Industrialists at Trinity College, Oxford, April 8–18, 1967, p. 12–17, footnote p. 12–53. This published result is correct to only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished. For a detailed account of calculations of sr see J. W. Wrench, Jr., “The evolution of extended decimal approximations to r,” The Mathematics Teacher, v. 53, 1960, p. 644–650.
F. Genuys, “Dix milles decimales de sr,” Chiffres, v. 1, 1958, p. 17–22.
This unpublished value of 7 to 16167D was computed on an IBM 704 system at the Commissariat à l’Energie Atomique in Paris, by means of the program of Genuys.
C. Störmer, “Sur l’application de la théorie des nombres entiers complexes à la solution en nombres rationnels, z,, zs, • • •, x„, c,, c,, • •, c,,, k de l’équation c, arctg z, + ci arctg zs + • • • + c,, arctg x„ = ksr/4,” Archiv for Mathematik og Naturvidenskab, v. 19, 1896, p. 69.
C. F. Gauss, Werke, Göttingen, 1863; 2nd ed., 1876, v. 2, p. 499–502.
S. Ramanujan, “Modular equations and approximations to sr,” Quart. J. Pure Appl. Math., v. 45, 1914, p. 350–372; Collected papers of Srinivasa Ranw.nujan, Cambridge, 1927, p. 23–39.
Note added in proof, December 1, 1961. J. M. Gerard of IBM United Kingdom Limited, who was then unaware of the computation described above, computed sr to 20,000 D on the 7090 in the London Data. Centre on July 31, 1961. His program used Machin’s formula, (1), and required 39 minutes running time. His result agrees with ours to that number of decimals.
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© 1997 Springer Science+Business Media New York
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Shanks, D., Wrench, J.W. (1997). Calculation of π to 100,000 Decimals. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2736-4_38
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DOI: https://doi.org/10.1007/978-1-4757-2736-4_38
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