Michael Coen, last seen here, told me this amusing story. In the Torah, there’s a verse that describes a certain pool in the temple as being 10 cubits across and 30 cubits in circumference — in other words, pi = 3. On the other hand, as the Vilna Gaon observed, the word meaning “circumference” here is spelled “kuf vav hay,” where it would normally be spelled “kuf vav.” The standard spelling has an alphanumeric value of 106, but the variant used in the verse has a slightly larger value, 111. If you “correct” the estimate 3 by a factor of 111/106, you get 333/106 = 3.1415…, the third continued fraction approximant to pi.
Clever dudes, those Torah scholars.