Sunday 10 March 2024

464) Interesting math in the Hebrew Bible


Guest Post by Professor Larry Zamick

There are numerous examples in the Bible of lists of numbers with totals that don't add up correctly. For example, when God asked Moses to count the descendants of Levi, the results were given in a table. 


In Numbers 3.21 it says the clan of Gershon consisted of 7500.In Numbers 3.27-28 it says that that in the clan of Korach there were 8600.Finally in Numbers 3.33-34 the clan of Meran had 6,200members. Add that up:

7500+8600+6200 = 22,300.  But in Numbers 3.39 it says the total is 22,000.

For a normal document this would not be such a big deal-it could even be a roundup error. But this is the Hebrew Bible. 


In Chronicles 3:22 - And the sons of Shechaniah; Shemaiah: and the sons of Shemaiah; Hattush, and Igeal, and Bariah, and Neariah, and Shaphat, six.

Though only five sons of Shemaiah are listed, it says there are six. This may just be a copyist error where one of the sons' names was omitted.


In Kings 1: " Solomon’s pool has 2000 baths of water". But in Chronicles 2:   " 3000 baths of water." The solution to this discrepancy is that Kings 1 refers to the amount of water actually in the pool whereas Chronicles 2 refers to the maximum capacity of the pool.


It says In First Kings that Jehoiachin was anointed king of Judah when he

was 8 but in 2 chronicles it says he was anointed when he was 18.

We don’t know the precise answer to this discrepancy but the story of King

David might give us a clue. David was anointed 3 times-once when he was

a teenager, second when he was king of only a few tribes and finally when

he became king of all the tribes. So there is a precedence for kings to be

anointed more than once.


1 Kings 7:23 - And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.

Claim: This describes the ratio of the circumference to the diameter, which we all know is pi = 3.14159…

But the above comments in Kings and Chronicles gives the value as three.

What went wrong?

There is an answer given by Kevin Pell in a letter to the leading scientific magazine -Nature. Basically, he says that for an infinitely thin pipe the objection would be correct. But: 

“Assuming that a cubit measures 18 inches and a handbreadth 3 inches,

the inner diameter of the bowl would be 174 inches and the inner

circumference would be 540 inches. This yields a value of pi of

540/174 = 3.1. This is about a 1% error from the typical value of pi of

3.14. Although we don’t know the exact value of a cubit or a

handbreadth, this is very close to the exact value of pi.”

Kevin Pell, Reactor engineering group. Dow Chemical Company.”




This Shabbat morning our Rabbi made some comments which can be turned into a

math quiz, quite seriously.

To paraphrase a bit if you have a barrel of grain and you take n scoops out how much

grain do you have left?

To make things simple suppose there is 1 kilo of grain and x is the amount of grain taken


Take away x. (or 100x %).

Left over (1-x)


take away x (1-x)

Left over (1-x) -x(1-x) =1 -2x+ x2= (1-x)2

Step 3.

Take away:  × (1-2x +×2 )

Left over: (1-x) -x (1-x) -x (1-2x+×2) =1-3× +3x23 =(1 -x)3

So we can generalize:

For n scoops you are left with (1-x)n of grain in the barrel.

Suppose x=0.1

For 10 scoops you are left with (0.9)n =34.86% of the grain still in the barrel.

If we did things differently and took the same amount -Å~%-each time then after 10

scoops the barrel would be empty (1-0.1*10 =0.) This exactly was the point the Rabbi

wanted to make.



Distance from Highland Park, NJ to New York
using Shabbat end times.
Jan 6, 2024
New York. Shabbat ends at 5.29 PM
Highland Park. 5.31 PM
Difference 2 minutes.
Circumference of earth 24,901 miles.
but we are at a latitude of 40.7 degrees. so must multiply by cos(40.7)=0.758
Time for Earth complete rotation. 24 hours = 1440 minutes.
So in 2 minutes you go 2/1440m*24901 *.758= 26.2 miles
My artificial intelligence says distance is 35.7 miles.
Why the discrepancy?
 It turns out that 35.7 miles is the driving distance.
The straight line distance is 28 miles.


  1. How do 10 amos of 18 inches become 174 inches and not 180 inches?

  2. Thank you for your question. I have forwarded it to the author.

  3. This is the reply from the author:

    Thank you for your interest.
    You are correct that the diameter is 10 * 18 = 180 inches, however this is the outer diameter. Mr. Pell wants the inner diameter. So, he subtracts 2 handbreadths-one from the top and one from the bottom. A handbreadth is 3 inches. So, we get 180-3-3 =174 inches.
    However, looking more carefully about what Mr. Pell wrote I think there is an error; he writes " the inner diameter of the bowl would be 174 inches and the inner circumference would be 540 inches."
    But it should say "outer circumference". That is, he takes the ratio of the outer circumference to the inner diameter in order to get a ratio of 3.1.
    So, thanks again-your comment has helped to clarify the situation.

  4. You cannot learn the value of Pi from an inner diameter and an outer circumference.
    If we say the verse is referring to an inner diameter and an outer circumference, then the verse can be describing a real object and not be saying Pi is 3.

  5. This is the reply from the author:

    You are right and Mr. Pell did not make a mistake. My apology.
    He indeed took the ratio of the inner circumference to the inner
    diameter. 540/ (180-3--3) = 3.1. This is close to pi.
    Your explanation is also plausible-that the number quoted in the bible is the
    inner circumference / outer diameter and is not expected to be pi. It is in fact 3.
    What is not clear to me is the meaning of the phrase " and a line of thirty cubits did compass it round about ".Is that an inner circumference or an outer circumference?
    By the way my mother told me never to argue someone called Yitzchok.