One excerpt, however, from the Bible suggests that, in ancient times, Israelite builders and land surveyors were working with much cruder approximations. Referring to the construction of the basin used for priestly ablutions in the temple of Solomon, the first book of Kings states: “And he made the molten sea of ten cubits from brim to brim, round in compass, . . . and a line of thirty cubits did compass it round about.” (1 Kings 7:23.) If one calculates the ratio between the thirty-cubit circumference of the “molten sea” and its ten-cubit diameter, it appears that the Bible’s redactors used the ratio 3:1 as a rough approximation for π. But what if the scribes who redacted 1 Kings knew that the value for π indicated in the text was merely an approximation? If so, how might they have signaled that awareness? Perhaps by using gematria, a hermeneutical technique whereby the numerical value of a letter is calculated based on its position in the Hebrew alphabet.
Significantly, in the text translated above from 1 Kings, the word “line” is used for “circumference” (“a line of thirty cubits did compass it round about”). In Hebrew, the word for “line” is qava, and it is usually spelled using the Hebrew letters quf and vov (many Hebrew words are spelled without vowels). But in 1 Kings, the word “line” is spelled incorrectly as qavah, using the Hebrew letters quf, vov, and hei. If each letter is given a numerical value based on its position in the Hebrew alphabet, then the value of qava (the correct spelling) is 100 + 6, or 106, but the value of qavah (the incorrect spelling) is 100 + 6 + 5, or 111. Thus, the text misspells qava, and the misspelling results in an error in the numerical value of that word, changing its value from 106 to 111.
Taking this bit of gematria into consideration, it appears that the scribes who redacted 1 Kings chose a very efficient way to express the value of π in the biblical text. Decimal notation was not in use at the time, and therefore if they had wanted to write that the “molten sea” was ten cubits across and 31.415 cubits around (which, of course, would have much more accurately approximated π), they would have needed to express 31.415 as the ratio 333:106 multiplied by 10, which would have required a great deal of additional text.