If something has a diameter of 10 cubits, what is its circumference? We all learn at school: take the diameter (10) times Pi, so we get 31.415 and small change. What does this have to do with the Torah? Simple, there is a verse in I Kings 7:23 where it seems that King Solomon (or whoever wrote it down) got his maths wrong:

And he made the molten sea of ten cubits from brim to brim, round in compass, and the height thereof was five cubits; and a line of thirty cubits did compass it round about.

(I Kings 7:23)

What do most people think? Easy, the number 30 given in the text is just an approximation when you approximate Pi by 3. Case closed. However, you can apparently prove from this that the Torah must be divine, because it contains the value for Pi. How? Well…

The word circumference is kav (written as kuf vav) in Hebrew, but in this verse it is written with an extra he at the end. There are several occurrences in the Torah where you pronounce something different than what is written, this is called kri vs. ktiv. Some people argue that there is hidden meaning in them. So in this case Pi is hidden in there and finding it works like this:

- The numerical value of “kuv vav” is 106 (kuf = 100, vav = 6).
- The numerical value of “kuv vav he” is 111 (kuf = 100, vav = 6, he = 5).
- 111 / 106 = 1.04716981132
- Pi / 3 = 1.0471975512

These ratios are the same, so the exact value of Pi is hinted in this verse – because G-d put it there.

First obvious objection: But the two numbers are not the same, they differ after the fifth decimal! TrueTorah replies that the thickness of the walls of the vesser may not be included in the calculation or that the vessel may not have been perfectly round. This does not really make a lot of sense, why would a hint to Pi be included in the description of an object that is not really round? And if there is some sort of approximation going on – why start any explaining? We could stay with the face value of 30 being an approximation.

Next objection: Why wouldn’t the ratio be Pi directly, Why Pi divided by 3? Why not use 106/111? Why 3 and not 2 or 4? Too many degrees of freedom, a statistician would say. There are many other fractions that give an approximate value for Pi (Comment by nachman on December 29, 2013 at 8:15 PM). And if you are free to change nominator and denominator or multiply a fraction with other things, there are many many possibilities of finding something. Or something else (tomorrow’s stock values anybody?).

And the next objection: The Vilna Gaon is credited with this interpretation. Wikipedia says he lived in the 18th century. The source given in the TorahTrue article is a journal article from 1962! Good values for Pi have been known earlier, we can assume Jewish scholars knew them as well. So why did nobody notice this before? And if it is that difficult to find, why put it there in the first place?

Last objection: Even if we accept this is a reference to Pi, it does not prove that G-d put it there. The old Greeks and Egyptians knew that the ratio between a diameter and a circumference of a circle is fixed and calculated various approximations (Pi – Antiquity). So a maths freak might have put the reference into the text as an inside joke

( Happy Pi Day ).

So I really don’t think you can make an argument for the divinity of the Torah out of this. This does not mean that the Torah is not divine either or that there is no G-d. Just that this is a stupid argument and should not be used to convince people to believe in Judaism.

Happy Pi day!

Note: This post was scheduled to appear on Pi day even though it is shabat, but written beforehand.

Danny Kogan

said:“Why wouldn’t the ratio be Pi directly, Why Pi divided by 3”

The idea of this wort (wouldn’t call it proof) is that the difference between kri and ktiv is the different between the realistic approximation and the ideal, just like the difference between the ideal ratio (pi) and the realistic approximation ratio (3).