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Archive for History of Exact Sciences

, Volume 26, Issue 2, pp 115–126 | Cite as

Wallis's product, Brouncker's continued fraction, and Leibniz's series

  • Jacques Dutka
Article

Abstract

A historical sketch is given of Wallis's infinite product for 4/π, and of the attempts which have been made, over more than three centuries, to find the method by which Brouncker obtained his equivalent continued fraction. A derivation of Brouncker's formula is given. Early results obtained by Indian mathematicians for the series for π/4, later named for Leibniz, are reviewed and extended. A conjecture is made concerning Brouncker's method of obtaining close bounds for π.

Keywords

Early Result Continue Fraction Close Bound Infinite Product Indian Mathematician 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag GmbH & Co. KG 1982

Authors and Affiliations

  • Jacques Dutka
    • 1
  1. 1.Audits & Surveys, Inc.New York City

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