CTK Insights

09 Aug

Biblical π and Gematria

According to [P. Beckmann, p. 12], by 2000 BC, the ancient Babilonians already new that π is close to 25/8 (≈ 3.125), while the Egyptians estimated it as 4(8/9)² (≈ 3.1605). Beckmann, as many others, do not conceal his astonishment that in the Bible the apparent estimate is a simplistic 3. This is based on two biblical passages (I Kings, vii.23, and II Chronicles iv.2) that could be translated as:

And he (Solomon) made a molten sea, ten cubits from one brim to the other: it was round all about, and its height was five cubits; and a line of thirty cubits did compass it round about.

Here is a reconstruction of the vessel which was metaphorically called sea due to its big size

Clearly, if the diameter of the sea is given as 10 cubits and the circumference as 30 cubits, the π estimate is the embarrassing 30/10 = 3.

In 1985, M. D. Stern questioned this reading. I believe Stern's reasoning deserves to be known better.

I have two versions of the Old Testament. In the two, the Chronicle's variants are identical, while Kings' variants differ slightly but significantly. In addition, the Chronicle's variant differs from one of the Kings' variants in a single word. The other variant elaborates on this difference. Let me explain.

The most expansive version of that passage is from one of the editions of I Kings:

All the differences between several versions are focused at a few words circled below

In both versions of Chronicles there appears just one word:

Like this:

In one variant of Kings there is also one single word and this is

Like this:

In the full quote above both words appear (one in parentheses). Let me observe that Hebrew is written and read right-to-left. The letter ו preceding the two words simply means "and" and is not part of the words, although it is written with no space between them.

So what are those words קו and קוה, and what is the difference between them?

First of all, the first - קו - is a Hebrew word whose meaning is a line (see the English translation above.) The second word - קוה - has a double meaning: a) collect water; b) hope, neither of which fits the translated interpretation. When קוה appears in the variant of Kings above, it is followed by an injunction (in parentheses) to treat it as if it were קו. But if its meaning does not fit the rest of the text, why is the word there in the first place?

The ancient Hebrews (as did the ancient Greeks) used letters to denote numbers. The 22 letters of the alphabet have been assigned successive values 1 through 9, then 10 through 90 and then 100 through 400. (Note that all the letters are consonants, the vowels are not considered letters; you can see them as dots and short lines just below the consonants. Vowels are often omitted.)

Every Hebrew word can be considered a number - gematria of the word. Thus, for example, the gematria of word קו is 106. On the other hand, קוה signifies the number 111. It was M. D. Stern's insight to suggest that both letter combinations קו and קוה should be seen as numbers and not as words.

In other words, the expression which is translated as "a line of thirty" should be read as "111 (treated as 106) times 30" which would introduce a correction factor of 111/106, implying the estimate

3·111/106 ≈ 3.141509

which is within 10-4 of the correct value.

Beckmann observes that the wise people of Talmud (c. 500 AD) still insisted on the wrong value of 3, but opines that this is probably an early case of divergence between science and religion:

By the time the Old Testament was edited, the two (science and religion) were already separated. The inaccuracy of the biblical value of π is, of course, no more than an amusing curiosity. Nevertheless, with the hindsight of what happened afterwards, it is interesting to note this little pebble on the road to confrontation between science and religion, which on several occasions broke into an open conflict ...

Who knows? Chronicles that use קו are of a later origin than Kings that feature קוה. Perhaps, the composers of the former already on that early stage dared to set things straight without actually understanding or caring for what they were doing.


  1. P. Beckmann, (a history of) π, St. Martin's Press, 1971
  2. M. D. Stern, A remarkable approximation to π, The Mathematical Gazette, v 69, n 449 (Oct 1985), 218-219

One Response to “Biblical π and Gematria”

  1. 1
    Fritz Zimmerman Says:

    Did the Gematria Codes determine when Christs was Crucified? Some insight in to the number 33 here.


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