The square root of to 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.

**[1]**René Coustal,*Calcul de √2, et réflexion sur une espérance mathématique*, C. R. Acad. Sci. Paris**230**(1950), 431–432 (French). MR**0033181****[2]**Horace S. Uhler,*Many-figures approximations to √2, and distribution of digits in √2 and 1/√2*, Proc. Nat. Acad. Sci. U. S. A.**37**(1951), 63–67. MR**0038717****[3]**K. Takahashi & M. Sibuya, ``The decimal and octal digits of ''*Math. Comp.*, v. 21, 1967, pp. 259-260.**[4]**M. Lal, ``Expansion of to 19600 decimals,''*Math. Comp.*, v. 21, 1967, pp. 258-259.**[5]**M. Lal, ``First 39000 decimal digits of ,''*Math. Comp.*, v. 22, 1968, p. 226.**[6]**M. Lal & W. F. Lunnon, ``Expansion of to 100,000 decimals,''*Math. Comp.*, v. 22, 1968, pp. 899-900.**[7]**Trygve Nagell,*Introduction to number theory*, Second edition, Chelsea Publishing Co., New York, 1964. MR**0174513****[8]**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

DOI:
https://doi.org/10.1090/S0025-5718-1971-0298857-0

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

Article copyright:
© Copyright 1971
American Mathematical Society