William Shanks

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William Shanks
Born (1812-01-25)January 25, 1812
Corsenside, Houghton-le-Spring, city of Sunderland, Tyne and Wear, England
Died 1882 (aged 70)
Houghton-le-Spring, city of Sunderland, County Durham, England
Fields Amateur calculator, school owner

William Shanks (January 25, 1812 – June 1882, Houghton-le-Spring, city of Sunderland, Tyne and Wear, England)[1] was a British amateur mathematician.

Shanks is famous for his calculation of π to 707 places, accomplished in 1873, which, however, was only correct up to the first 527 places.[2] This error was highlighted in 1944 by D. F. Ferguson (using a mechanical desk calculator).[3]

Shanks earned his living by owning a boarding school at Houghton-le-Spring, which left him enough time to spend on his hobby of calculating mathematical constants. His routine was as follows: he would calculate new digits all morning; and then he would spend all afternoon checking his morning's work. To calculate π, Shanks used Machin's formula:

 \frac{\pi}{4} = 4 \arctan \left(\frac{1}{5} \right) - \arctan \left(\frac{1}{239} \right)

Shanks' approximation was the longest expansion of π until the advent of the electronic digital computer about one century later.

Shanks also calculated e and the Euler–Mascheroni constant γ to many decimal places. He published a table of primes up to 60 000 and found the natural logarithms of 2, 3, 5 and 10 to 137 places.

Shanks died in Houghton-le-Spring in summer 1882, aged 70, and was buried at the local Hillside Cemetery on June 17, 1882.[4]

See also[edit]

References[edit]

  1. ^ GRO Register of Deaths: JUN 1882 10a 252 HOUGHTON - William Shanks, aged 70
  2. ^ Smyth, Chris (January 7, 2010). "Pi a mathematical story that would take 49000 years to tell". The Times (London). 
  3. ^ "Shank's Biography". School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 2012-10-30. 
  4. ^ Houghton le Spring Hillside Cemetery

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