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Calculation of $ \pi $ to 100,000 decimals


Authors: Daniel Shanks and John W. Wrench
Journal: Math. Comp. 16 (1962), 76-99
MSC: Primary 65.99
DOI: https://doi.org/10.1090/S0025-5718-1962-0136051-9
MathSciNet review: 0136051
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  • [1] G. Reitwiesner, ``An ENIAC determination of $ \pi $ and e to more than 2000 decimal places,'' MTAC, v. 4, 1950, p. 11-15. MR 0037597 (12:286i)
  • [2] S. C. Nicholson & J. Jeenel, ``Some comments on a NORC computation of $ \pi $,'' MTAC, v. 9, 1955, p. 162-164. MR 0075672 (17:789b)
  • [3] 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, 1957, 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only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished.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 $ \pi $ see J. W. Wrench, Jr., ``The evolution of extended decimal approximations to $ \pi $,'' The Mathematics Teacher, v. 53, 1960, p. 644-650.
  • [4] F. Genuys, ``Dix milles decimales de $ \pi $,'' Chiffres, v. 1, 1958, p. 17-22. MR 0094928 (20:1436)
  • [5] This unpublished value of $ \pi $ to 16167D was computed on an IBM 704 system at the Commissariat à l'Energie Atomique in Paris, by means of the program of Genuys.
  • [6] C. Störmer, ``Sur l'application de la théorie des nombres entiers complexes à la solution en nombres rationnels, $ {x_1},\,{x_2},\, \cdot \cdot \cdot ,{x_n}$, $ {c_1},\,{c_2},\, \cdot \cdot \cdot ,\,{c_n}$, k de l'équation $ {c_1}$ $ \operatorname{arctg}\,{x_1}\, + \,{c_2}$ $ \operatorname{arctg}\,{x_2}\, + \, \cdot \cdot \cdot + \,{c_n}$ $ \operatorname{arctg}\,{x_n}\, = \,{k\pi }/{4}$,'' Archiv for Mathematik og Naturvidenskab, v. 19, 1896, p. 69.
  • [7] C. F. Gauss, Werke, Göttingen, 1863; 2nd ed., 1876, v. 2, p. 499-502.
  • [8] S. Ramanujan, ``Modular equations and approximations to $ \pi $,'' Quart. J. Pure Appl. Math., v. 45, 1914, p. 350-372; Collected papers of Srinivasa Ramanujan, Cambridge, 1927, p. 23-39. MR 2280849

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DOI: https://doi.org/10.1090/S0025-5718-1962-0136051-9
Article copyright: © Copyright 1962 American Mathematical Society

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