Career
This error was highlighted in 1944 by Doctorate. 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:
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.