Today, March 14th, is official Pi Day. (The date is chosen because it's 3.14.) You can check out this link for a brief history of Pi. Meanwhile, I'd like to share a few thoughts about Pi in Jewish thought. I have not been able to research this topic anywhere near as thoroughly as I usually do, but I don't want to miss the date, so here are some thoughts.
There are those who claim that the description of King Shlomo's Pool having a diameter of 10 cubits and a circumference of 30 cubits is an example of a scientific error in the Bible. Now, I am certainly not ideologically closed to the idea of the Bible being scientifically inaccurate - there are several examples of this, such as with the kidneys, dew, firmament, etc., for which we invoke the concept of Dibra Torah k'lashon bnei Adam. However, I don't believe that King Shlomo's Pool is an example of this; it's just a convenient way of describing it. Although, it is perhaps a little problematic here because instead of saying that its circumference was 30 cubits, it says that a thirty-cubit line could encircle it.
A few days ago, a reader who is convinced that Chazal had a supernatural source of knowledge about the natural world gave King Shlomo's Pool as an example. Here is the idea, as presented by Rav Mordechai Kornfeld (and follow the link for further discussion):
A fascinating insight regarding the value of pi is attributed to the Vilna Ga'on. (Actually, there is no source to substantiate the claim that the Vilna Ga'on said it. The actual source for the insight may be credited to Matityahu ha'Kohen Munk (Frankfurt-London), who published the thought in the journals "Sinai," Tamuz 1962, and "ha'Darom," 1967.) In the verse that the Gemara cites as the source for the ratio of the circumference to the diameter (Melachim I 7:23), there is a "Kri" and a "Kesiv" -- a word that is pronounced differently than it is spelled. The word in the verse is written "v'Kaveh" (with the letter "Heh" at the end), but it is pronounced "v'Kav" (with no "Heh" at the end). The Gematriya of the word "Kav" is 106, and the Gematriya of the word "Kaveh" is 111. The ratio of the Kesiv (111) to the Kri (106), or 111/106, is 1.0471698. This value represents the ratio of the value for pi to 3 (3.1415094/3 = 1.0471698).
The question is, does this provide evidence for Chazal having supernatural sources of knowledge? I don't think so, for several reasons.
First of all, a person could argue that the kav/kaveh curio is simply a coincidence. It's not a matter of something being accurate to seven decimal places. There are two numbers, 106 and 111, which can be manipulated to give a certain value. There are doubtless plenty of two and three digit numbers which can be manipulated to give a similar value, and there are plenty of two and three digit numbers that can be derived from a verse. Some will see this as unduly skeptical, and at the moment, I am inclined to agree, since it's just too neat that it's exactly with the word describing the circumference that this gematria is found. But I don't think that I can conclusively show that it's not a coincidence.
As for the significance of the kri/ksiv, while Malbim and (of course) Maharal ascribe significance to both kri and ksiv, according to Radak they simply reflect uncertainties that arose in transmission.
Then, even if one wants to claim that Pi is encoded in kav/kaveh, does this reflect a supernatural encoder? The value of Pi was known in ancient times to several decimal places, and a human could encode it in this way. There is a Greek Pythagorean motto "God is ever a geometer" (ἀεὶ ὁ Θεὸς ὁ μέγας γεωμετρεῖ) — the number of letters in each of the six words are the first six digits of pi. A cute and deliberately constructed device, but not one that indicates that the composer of either the phrase or the language was supernatural!
Finally, even if one does feel that this strongly points to a supernatural encoder, it is not evidence of Chazal possessing a supernatural source of knowledge. The verse is assumed to have been written with Divine Inspiration, which means that God has supernatural knowledge, not man. With regard to Chazal, it does not appear that they knew the value of Pi to any decimal places. The Gemara gives the value of Pi as being 3 (Eruvin 14a), and Tosafos points out that, based on the context, the Gemara does not seem to be giving an approximation. Of course, there are various apologetics which argue otherwise, but Tosafos apparently didn't find them convincing. Thus, if someone wants to believe that the Gemara did not mean this, they can do so, but one cannot use the topic of Pi to prove that Chazal had superior knowledge of the natural world.
Furthermore, the Mishnah (Ohalos 12:6) says that "A square is greater than a circle by one-fourth," referring to the perimeter of each when the circle is drawn to the height of the square. This is true if Pi is assumed to be 3, but given a more accurate value of Pi, the perimeter of the square is actually closer to one-fifth longer than that of the circle.
Some readers will doubtless find it hard to accept that Chazal believed Pi to be 3. The question is whether there is basis for their disbelief, and an analysis of the Gemara and Rishonim reveals that there were much more basic mathematical errors committed by some (but not all) of Chazal. Tosafos (Eruvin 76a) says that Rabbi Yochanan and the Gemara in Sukkah misunderstood a statement by the judges of Caesarea to mean that the diagonal of a square is equal to twice the length of its side. Tosafos states that Rabbi Yochanan subscribed to this understanding of the judges of Caesarea, and that the Gemara in Sukkah rejected it precisely because it is mathematically inaccurate. Rashba expresses surprise at Tosafos attributing a simple mathematical error to Chazal, and he gives an alternate explanation, but he does not deny that Tosafos does indeed say this! Ran likewise expresses surprise that the judges of Caesarea erred in a simple mathematical matter, and cites an alternate explanation of Rabbi Yochanan’s misunderstanding of what the judges of Caesarea were saying, which somewhat lessens the error, but still leaves Rabbi Yochanan making genuine errors of both interpretation and mathematics. Tosafos HaRosh states similarly. Given all this, there is no reason not to take the Gemara's statement about the ratio of a circle's circumference to its diameter at face value.
Finally, we have Rambam on record as being the first person in recorded history to explicitly describe Pi as being an irrational number (see Wired Magazine's article on this). I don't know whether it is amusing or sad that some people co-opt the Rambam for anti-rationalist purposes. Jonathan Rosenblum declared that Rambam's statement about Pi is evidence that Torah scholars have supernatural sources of knowledge about the natural world. But first of all, while Rambam was the first to write this explicitly, it had already been hinted at by earlier Greek writers. Secondly, the idea that Rambam knew this via kabbalah or some other such source is ludicrous and a distortion of Rambam's fundamental ideology. Rambam himself wrote that even Chazal had no such supernatural sources of knowledge; he certainly did not consider himself to be privy to kabbalistic secrets!
Have a happy Pi day, and let's not undermine the credibility of Torah and Judaism by making extreme claims that do not stand up to scrutiny. There's enough to be proud of in our religion without having to resort to such shtick!
(See too the follow-up post from two years ago: Puzzled by Pi Perplexities)