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.
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