An ENIAC Determination of π and e to more than 2000 Decimal Places

  • George W. Reitwiesner

Abstract

Early in June, 1949, Professor John von Neumann expressed an interest in the possibility that the ENIAC might sometime be employed to determine the value of π and e to many decimal places with a view toward obtaining a statistical measure of the randomness of distribution of the digits, suggesting the employment of one of the formulas:
  • π/4 = 4 arctan 1/5 − arctan 1/239

  • π/4 = 8 arctan 1/10 − 4 arctan 1/515 − arctan 1/239

  • π/4 = 3 arctan 1/4 + arctan 1/20 + arctan 1/1985

in conjunction with the Gregory series
$$ \arctan \;x = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}} {(2n + 1)^{ - 1}}{x^{2n + 1}}. $$

Keywords

Decimal Place Successive Term Cumulative Total Check Sequence Aberdeen Prove Ground 
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 Science+Business Media New York 1997

Authors and Affiliations

  • George W. Reitwiesner
    • 1
  1. 1.Ballistic Research LaboratoriesAberdeen Proving GroundUSA

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