Merry π Day

Amidst the continued downward spiral and ongoing severity of world events, I needed a break to connect to something stable, constant, even if irrational. On the occasion of March 14th, we celebrate π Day on 3.14. Here is a very informative TED talk on the topic:

While we need to claim that we had it first, I was fascinated to find out recently how long ago our people engaged with this idea of Pi. Way back when in the book of Kings we learn about the Molten Sea or Brazen Sea. This was a large basin in the Temple in Jerusalem made by Solomon (990- 931 BCE)  for ablution of the priests. It stood in the south-eastern corner of the inner court. We read:

The structure of the laver stands was as follows: They had insets; and on the insets within the frames were lions, oxen, and cherubim. Above the frames was a stand; and both above and below the lions and the oxen were spirals of hammered metal. Each laver stand had four bronze wheels and [two] bronze axletrees. Its four legs had brackets; the brackets were under the laver, cast. Its funnel, within the crown, rose a cubit above it; this funnel was round, in the fashion of a stand, a cubit and a half in diameter. On the funnel too there were carvings. But the insets were square, not round. And below the insets were the four wheels. The axletrees of the wheels were [fixed] in the laver stand, and the height of each wheel was a cubit and a half. The structure of the wheels was like the structure of chariot wheels; and their axletrees, their rims, their spokes, and their hubs were all of cast metal. Four brackets ran to the four corners of each laver stand; the brackets were of a piece with the laver stand. At the top of the laver stand was a round band half a cubit high, and together with the top of the laver stand; its sides and its insets were of one piece with it. On its surface—on its sides—and on its insets [Hiram] engraved cherubim, lions, and palms, as the clear space on each allowed,-d with spirals round about.

I Kings 7: 28- 36

Here is an artistic representation of what it might have looked like:

An artist’s rendition of the Molten Sea

The biblical description that the bowl has a diameter of 10 cubits and a circumference of 30 cubits suggest that in the construction of the basin, π was approximated with the integer value 3. This is consistent with the practice in Babylonian mathematics at the time (6th century BC), but it has given rise to debate within rabbinical Judaism from an early period due to the concern that the biblical text might here be inaccurate. Rabbi Nehemiah in the 2nd century argued that the text is not claiming that π equals 3, but that instead the Israelites measured the diameter from the outside edge of the rim of the bowl. After accounting for the width of the brim—”about an hand breadth”—this results in a ratio closer to the true value of π.

The Vilna Gaon pointed to the fact that the word for measuring line in the respective verses (1 Kings 7:23, 2 Chronicles 4:2) is written in two different ways, as קוה and קו. That hints to two different measures. If the Hebrew letters are read as numbers, the first form of the word for measuring line adds to 111 and the second form to 106. The relation i.e. the quotient of these two measuring tapes is 1.0472. And if this number, the relation of these two measuring tapes, is multiplied with Solomon’s simple π of 3, the result reads: 3.1416, much closer to the exact value of π.

It is easy to dispute all of these apologies for π, but sometimes amidst the chaos it is comforting to find meaning in things that are predictably irrational.

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