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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The square root of $2$ to $1,000,000$ decimals
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by Jacques Dutka PDF
Math. Comp. 25 (1971), 927-933 Request permission

Abstract:

The square root of 2 has been calculated to 1,000,000 decimals on a large-scale digital computer and the result has been verified. The calculation was based on a specially developed algorithm for square roots which does not appear to have been used in previous computations of this type.
References
  • René Coustal, Calcul de $\sqrt {2}$, et réflexion sur une espérance mathématique, C. R. Acad. Sci. Paris 230 (1950), 431–432 (French). MR 33181
  • Horace S. Uhler, Many-figures approximations to $\sqrt {2}$, and distribution of digits in $\sqrt {2}$ and $1/\sqrt {2}$, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 63–67. MR 38717, DOI 10.1073/pnas.37.1.63
  • K. Takahashi & M. Sibuya, “The decimal and octal digits of $\surd n$” Math. Comp., v. 21, 1967, pp. 259-260. M. Lal, “Expansion of $\surd 2$ to 19600 decimals,” Math. Comp., v. 21, 1967, pp. 258-259. M. Lal, “First 39000 decimal digits of $\surd 2$,” Math. Comp., v. 22, 1968, p. 226. M. Lal & W. F. Lunnon, “Expansion of $\surd 2$ to 100,000 decimals,” Math. Comp., v. 22, 1968, pp. 899-900.
  • Trygve Nagell, Introduction to number theory, 2nd ed., Chelsea Publishing Co., New York, 1964. MR 0174513
  • J. R. Ehrman, A Multiple-Precision Floating-Point Arithmetic Package for System/ 360, Report CGTM18, Stanford Accelerator Center, 1967.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 927-933
  • MSC: Primary 65A05
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0298857-0
  • MathSciNet review: 0298857