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Computation of π Using Arithmetic-Geometric Mean

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Pi: A Source Book

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Abstract

A new formula for π is derived. It is a direct consequence of Gauss’ arithmetic-geometric mean, the traditional method for calculating elliptic integrals, and of Legendre’s relation for elliptic integrals. The error analysis shows that its rapid convergence doubles the number of significant digits after each step. The new formula is proposed for use in a numerical computation of π, but no actual computational results are reported here.

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References

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Authors and Affiliations

  1. Charles Stark Draper Laboratory, Cambridge, Massachusetts, 02139, USA

    Eugene Salamin

Authors
  1. Eugene Salamin
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© 2000 Springer Science+Business Media New York

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Salamin, E. (2000). Computation of π Using Arithmetic-Geometric Mean. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3240-5_46

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  • DOI: https://doi.org/10.1007/978-1-4757-3240-5_46

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-3242-9

  • Online ISBN: 978-1-4757-3240-5

  • eBook Packages: Springer Book Archive

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