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

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

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