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To some extent, the progress of mathematics&mdash;or at least of computation&mdash;can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated.  

To some extent, the progress of mathematics&mdash;or at least of computation&mdash;can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated.  

In the ancient world it was common, and often sufficient, to express the relationship between  the circumference of a circle and its diameter as an integer ratio, 3:1. For example, 1 Kings 7:23 contains the passage "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about." One of the less seiorus arguments made against Biblical inerrancy is that the 3:1 ratio does not permit a precise calculation of the value of pi.  Many counterarguments exist<ref>Assuming that: the "sea" is perfectly circular; the measurements are to be understood as exact; the measurement of the "compass" and across the "brim" are measurements of the same circle, rather, than say, exterior and interior measurements of a wide lip; etc.</ref><ref>Rounding was standard procedure in the ancient world. [http://www.tektonics.org/lp/piwrong.html Is the Bible Wrong About Pi?]</ref>, including the fact that pi is irrational (and hence impossible to represent exactly in decimal or fractional form), as well as the observation that nowhere does the Bible set out to provide its readers with the values of mathematical constants.

In the ancient world it was common, and often sufficient, to express the relationship between  the circumference of a circle and its diameter as an integer ratio, 3:1. For example, 1 Kings 7:23 contains the passage "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about." One of the less serious arguments made against Biblical inerrancy is that the 3:1 ratio does not permit a precise calculation of the value of pi.  Many counterarguments exist<ref>Assuming that: the "sea" is perfectly circular; the measurements are to be understood as exact; the measurement of the "compass" and across the "brim" are measurements of the same circle, rather, than say, exterior and interior measurements of a wide lip; etc.</ref><ref>Rounding was standard procedure in the ancient world. [http://www.tektonics.org/lp/piwrong.html Is the Bible Wrong About Pi?]</ref>, including the fact that pi is irrational (and hence impossible to represent exactly in decimal or fractional form), as well as the observation that nowhere does the Bible set out to provide its readers with the values of mathematical constants.

Some ancients expressed pi more precisely 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 vaue 22/7 (3 1/7) is still used today.

Some ancients expressed pi more precisely 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 (3 1/7) 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>

[[Archimedes|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: within 0.04% of pi.

He said it was between 223/71 and 22/7. This is ten times better than the Egyptian and Babylonian values: within 0.04% of pi.