to a great many decimal
places. He published a table of primes up to 60 000, found
the natural logarithms of 2, 3, 5 and 10 to 137 places and the values of
212m+1 for m = 1, 2, 3, ..., 60.
William Shanks kept a boarding school at Houghton-le-Spring in a coal mining area near Durham, England.
Shanks is famed for his calculation of p to 707 places in 1873, which unfortunately was only correct for the first 527 places. He used the formula
p/4 = 4 tan-1(1/5) - tan-1(1/239).
Shanks also calculated e and Euler's
constant to a great many decimal
places. He published a table of primes up to 60 000, found
the natural logarithms of 2, 3, 5 and 10 to 137 places and the values of
212m+1 for m = 1, 2, 3, ..., 60.
In 1944 Ferguson calculated p using the formula
p/4 = 3 tan-1(1/4) + tan-1(1/20) + tan-1(1/1985).
He found that his value disagreed with that of Shanks in the
528th place. Ferguson discovered that Shanks had omitted two terms
which caused his error.