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Mathematics of Computation

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The square root of $2$ to $1,000,000$ decimals


Author: Jacques Dutka
Journal: Math. Comp. 25 (1971), 927-933
MSC: Primary 65A05
DOI: https://doi.org/10.1090/S0025-5718-1971-0298857-0
MathSciNet review: 0298857
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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 [Enhancements On Off] (What's this?)

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  • 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 https://doi.org/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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Keywords: Square root of 2, quadratically convergent algorithm, Pell equation
Article copyright: © Copyright 1971 American Mathematical Society