ผู้ใช้:Loma

จาก ThaiL10N

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. Article by: J J O'Connor and E F Robertson