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On Rational Function Approximations to Square Roots

by M. J. Jamieson

This article originally appeared in:
American Mathematical Monthly
January, 1999

Subject classification(s): Algebra and Number Theory | Number Theory | Calculus | Single Variable Calculus | Limits
Applicable Course(s): 4.3 Number Theory

Using a result on periodic continued fractions, the author presents a rational function method of approximating square roots that is faster than Newton's method.

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Capsule Course Topic(s):
Number Theory | Continued Fractions
Number Theory | Number Sequences
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