William Shanks

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William Shanks
Born(1812-01-25)25 January 1812
Died1882 (aged 70)
Scientific career
Fieldsschoolmaster, mathematician
InstitutionsSchool at Houghton-le-Spring
Shanks' approximation to π, published in 1853

William Shanks (25 January 1812 – June 1882)[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][3] This error was highlighted in 1944 by D. F. Ferguson (using a mechanical desk calculator).[4]

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:

Shanks's approximation was the longest expansion of π until the advent of the digital electronic 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, County Durham, England in June 1882, aged 70, and was buried at the local Hillside Cemetery on 17 June 1882.[5]

See also[edit]


  1. ^ GRO Register of Deaths: JUN 1882 10a 252 HOUGHTON – William Shanks, aged 70
  2. ^ "William Shanks (1812 - 1882) - Biography - MacTutor History of Mathematics". Archived from the original on 2021-02-05.
  3. ^ Berlinghoff, William P.; Gouvea, Fernando Q. (2020). Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition (illustrated, revised ed.). American Mathematical Soc. p. 110. ISBN 978-1-939512-12-3.
  4. ^ "Shanks's Biography". School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 2012-10-30.
  5. ^ Houghton le Spring Hillside Cemetery

External links[edit]