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

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Pi: A Source Book

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

$$\arctan x = \sum\limits_{n - 10}^\infty {{{( - 1)}^n}{{(2n + 1)}^{ - 1}}{x^{2n + 1}}} $$

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Reitwiesner, G.W. (2000). An ENIAC Determination of π and e to more than 2000 Decimal Places. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3240-5_34

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  • DOI: https://doi.org/10.1007/978-1-4757-3240-5_34

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-3242-9

  • Online ISBN: 978-1-4757-3240-5

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