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Mathematicians have worked for centuries to calculate pi to more and more decimal places. To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which pi has been calculated.
Mathematicians have worked for centuries to calculate pi to more and more decimal places. To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which pi has been calculated.
Some ancients expressed pi by using fractional approximations. Papyrus of Ahmes, dated c. 1650 B.C., shows that ancient Egyptians had value 3 1/6 = 3.167). The Babylonian value from the same era was 3 1/8 = 3.125.<ref>Boyer, ''A History of Mathematics'', 2nd edition</ref> Both these values are accurate to within 1 percent. Note that the value 22/7 is still used today.
Some ancients expressed pi by using fractional approximations. Papyrus of Ahmes, dated c. 1650 B.C., shows that ancient Egyptians had value 3 1/6 (3.167). The Babylonian value from the same era was 3 1/8 = 3.125.<ref>Boyer, ''A History of Mathematics'', 2nd edition</ref> Both these values are accurate to within 1 percent. Note that the value 22/7 is still used today.
[[Archimedes]] of Syracuse (287-212 BC) carried out "the first theoretical calculation" of pi.<ref>[http://veling.nl/anne/templars/Pi_through_the_ages.html Pi through the ages]</ref> He said it was between 223/71 and 22/7. This is ten times better than the Egyptian and Babylonian values, and it is within 0.04 percent of the correct value. The German-Dutch mathematician Ludolph Van Ceulen used Archimedes's formula to calculate pi to 32 digits in 1615. He was so proud of his achievement that he had the digits engraved on his tombstone.
[[Archimedes]] of Syracuse (287-212 BC) carried out "the first theoretical calculation" of pi.<ref>[http://veling.nl/anne/templars/Pi_through_the_ages.html Pi through the ages]</ref> He said it was between 223/71 and 22/7. This is ten times better than the Egyptian and Babylonian values, and it is within 0.04 percent of the correct value. The German-Dutch mathematician Ludolph Van Ceulen used Archimedes's formula to calculate pi to 32 digits in 1615. He was so proud of his achievement that he had the digits engraved on his tombstone.