William Shanks

William Shanks
Born	25 January 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 (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] 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, city of Sunderland, Tyne and Wear, England in June 1882, aged 70, and was buried at the local Hillside Cemetery on 17 June 1882.^[4]

See also

• Chronology of computation of π
• History of π

References

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

External links

• Shank's biography at St.Andrews
• Article about Shanks in Houghton-le-Spring