Thursday, February 20, 2014

Pi in the Torah

This week, the הפטרה is read from מלכים א פרק ז. There is a difference of opinion as to which part of the פרק is read. The ספרדים and some אשכנזי shuls will read the part that contains a reference to the figure of π. פסוק כג states that the pool was 10 אמות in diameter and 30 אמות in circumference. The obvious difficulty is that π is more than 3. Even if the פסוק were to round to the nearest whole number, it would be 31.

There is a famous approach to this problem which is said over in the name of the גר"א although I am not sure there is any written evidence of it. The word used for the circumference is וקוה. However, it is read וקו. If you drop the leading ו which is simply a וי"ו החיבור, you are left with קו and קוה. The respective גמטריות of those words are 111 and 106. If you divide 111/106 and multiply that by the apparent figure of π used - 3 - then the result is 3.1415094! That is correct to 3 decimal places!

I once heard an interesting addendum to this. There needs to be some meaning behind the figure of 30 אמות. The thickness of the walls was 1/4 אמה (I'm not sure where we know that from.) Therefore, the inner diameter was 9 1/2 אמות. If you multiply that by π you come awfully close to 30. I thought heard this in the name of the מלבי"ם but I looked it up and he definitely did not say that.


  1. There is an in-depth essay on this matter here: of Solomon.htm

  2. I do not understand what do you find difficult?

    The text speaks about outer diameter (10 cubits), outer radius (or height, 5 cubits) and inner circumference (30 cubits).

    This in turn makes the thickness of the Sea [10-(30/Pi)] /2 = ~0.225 cubits or ~ 10.287cm or ~4.05 inches. Exactly an average handbreadth.

    Measure your hand with the ruler to confirm these calculations and you will find them very accurate.

    Here is a diagram that I made that shows the whole idea:

  3. קו is spelled differently in מלכים and דברי הימים.

    קו and קוה

    That's what makes the gematria work.