Mountain pass theorem

William Shanks (January 25, 1812 – June 1882, Houghton-le-Spring, city of Sunderland, Tyne and Wear, England) 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. This error was highlighted in 1944 by D. F. Ferguson (using a mechanical desk calculator).

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.

See also

• section "Numerical approximations" of the article on π
• Chronology of computation of π

References

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External links

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