Calculation of to 100,000 decimals

Authors:
Daniel Shanks and John W. Wrench

Journal:
Math. Comp. **16** (1962), 76-99

MSC:
Primary 65.99

MathSciNet review:
0136051

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**[1]**George W. Reitwiesner,*An ENIAC determination of 𝜋 and 𝑒 to more than 2000 decimal places*, Math. Tables and Other Aids to Computation**4**(1950), 11–15. MR**0037597**, 10.1090/S0025-5718-1950-0037597-6**[2]**S. C. Nicholson and J. Jeenel,*Some comments on a NORC computation of 𝜋*, Math. Tables Aids Comput.**9**(1955), 162–164. MR**0075672**, 10.1090/S0025-5718-1955-0075672-5**[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only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished.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 see J. W. Wrench, Jr., ``The evolution of extended decimal approximations to ,''*The Mathematics Teacher*, v. 53, 1960, p. 644-650.**[4]**François Genuys,*Dix mille décimales de 𝜋*, Chiffres**1**(1958), 17–22 (French). MR**0094928****[5]**This unpublished value of to 16167D was computed on an IBM 704 system at the Commissariat à l'Energie Atomique in Paris, by means of the program of Genuys.**[6]**C. Störmer,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, , ,*k*de l'équation ,''*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 𝜋 [Quart. J. Math. 45 (1914), 350–372]*, Collected papers of Srinivasa Ramanujan, AMS Chelsea Publ., Providence, RI, 2000, pp. 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