I was the headmaster for a boarding school at Houghton-le-Spring, a coal mining area near Durham, England. pi/4 = 4 arctan(1/5) - arctan(1/239).
I published a table of all the prime numbers less than 60,000.
I determined the natural logarithms of 2, 3, 5 and 10 to 137 places.
I am best known for my calculation of pi to 707 decimal places in 1873, using the formula:
Unfortunately, the mathematician Ferguson proved in 1944 that I had made an error in my approximation for pi in the 528th place.
William Shanks (1812-1882)