Shanks

William Shanks

Born: 25 Jan 1812 in Corsenside, Northumberland, England
Died: 1882 in Houghton-le-Spring, Durham, England

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Shanks kept a boarding school at Houghton-le-Spring in a coal mining area near Durham, England.

Shanks is famed for his calculation of pi to 707 places in 1873, which unfortunately was only correct for the first 527 places. He used the formula

pi/4 = 4 tan^-^1(1/5) - tan^-^1(1/239).

Shanks also calculated e and Euler's constant g to a great many decimal places. He published a table of primes up to 60 000, found the natural logarithms of 2, 3, 5 and 10 to 137 places and the values of 2^1^2^m^+^1 for m = 1, 2, 3, ..., 60.

In 1944 Ferguson calculated pi using the formula

pi/4 = 3 tan^-^1(1/4) + tan^-^1(1/20) + tan^-^1(1/1985).

He found that his value disagreed with that of Shanks in the 528th place. Ferguson discovered that Shanks had omitted two terms which caused his error.

References elsewhere in this archive:

Tell me about Shanks's part in evaluating pi

References:

  1. Dictionary of Scientific Biography
  2. A Fletcher, J C P Miller and L Rosenhead, An index of mathematical tables (London, 1962). 
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JOC/EFR February 1996