Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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NUMERICAL ANALYSIS OF CHORDS SUMMATION ALGORITHM FOR π VALUE

  • PARK, HYUN IL (Department of Chemical Engineering and Biotechnology, University of Cambridge) ;
  • PAHADIA, SAURAV (Department of Computer Science, University of Washington at Seattle) ;
  • HWANG, CHRISTINE (Department of Chemical & Biomolecular Engineering, Johns Hopkins University) ;
  • HWANG, CHI-OK (Division of Liberal Arts and Sciences, GIST College, Gwangju Institute of Science and Technology)
  • Received : 2019.12.09
  • Accepted : 2020.03.05
  • Published : 2020.05.30
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Abstract

We propose and analyze a chord summation algorithm, which combines the ideas of Viète and Archimedes to calculate the value of π. The error of the algorithm decreases exponentially per iteration and becomes pinched at a critical iteration, depending on the accuracy of the first input value, ${\sqrt{2}}$. The critical iteration is also analyzed.

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References

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