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 | References | Similar Articles | Additional Information

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.

- 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 https://doi.org/10.1073/pnas.37.1.63
K. Takahashi & M. Sibuya, “The decimal and octal digits of $\surd n$” - Trygve Nagell,
*Introduction to number theory*, 2nd ed., Chelsea Publishing Co., New York, 1964. MR**0174513**
J. R. Ehrman,

*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.

*A Multiple-Precision Floating-Point Arithmetic Package for System*/ 360, Report CGTM18, Stanford Accelerator Center, 1967.

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Additional Information

Keywords:
Square root of 2,
quadratically convergent algorithm,
Pell equation

Article copyright:
© Copyright 1971
American Mathematical Society