[Math Lair] William Shanks' Value of Pi

Math Lair Home > Topics > William Shanks' Value of Pi

In 1873, William Shanks calculated the value of π to 707 decimal places, a tremendous accomplishment in the days before computers or other mechanical aids to calculation. This remained the most precise value of π to be calculated for almost 75 years, until D. F. Ferguson used a desk calculator to calculate π to 808 decimal places. Making this calculation, Ferguson discovers that Shanks' calculation of π was wrong starting at the 528th decimal place. Below is the value that Shanks calculated for π, with the position of the first error in bold. You can see the correct value of π to 10,000 decimal places here.

π = 3.
    1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
    8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
    4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273
    7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094
    3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912
    9833673362440656643086021395016092448077230943628553096620275569397986950222474996206074970304123668
    8619951100892023837702131416941190298858254468163979990465970008170029631237738134208413079145118398
    0570985+