Surprisingly Accurate Rational Approximations

by Tom M. Apostol (California Institute of Technology) and Mamikon A. Mnatsakanian (California Institute of Technology)

Mathematics Magazine
October, 2002

Subject classification(s): Algebra and Number Theory | Number Theory | Analysis | Numerical Analysis
Applicable Course(s): 4.17 Numerical Analysis

This article presents rational approximations of $$\pi$$ and, in fact, any real number using continued fractions using the fact that the real number can expressed as the sum of its floor and fractional part, whose reciprocal can be expressed as the sum of its floor and fractional part, etc.

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