# Circular Reasoning

Topic: Approximations of Numbers in Bible

M. Stolzenbach from Brentwood, TN wrote:

Dear Rabbi,

A friend asked me about the description of the circular brass pool in the Temple. (I Kings, 7:23) Skeptics say that if this pool was 10 across and 30 around, then G-d doesn't seem to know the value of "pi." Either that, or the pool was not exactly circular.

One friend retorted (this was in e-mail) that approximate measurements are enough for some purposes. But my friend said that G-d certainly ought to know the exact facts, and this proved that the Bible was written by men, not by G-d. Can you help him, and me? (By the way, he liked your explanation concerning the evidence for the Exodus.) Thanks.

Dear M. Stolzenbach,

First let's define our terms: Pie is the relationship of one's belly button to one's belt buckle.

But seriously. The verse says that Solomon constructed a circular pool that was "ten cubits from edge to edge....and 30 around." The question is, how can this be? If it was ten across, it would be more than thirty around. (It would be closer to 31.4, a difference of 1.4 cubits, or approximately 3 feet.)

This has nothing to do with "knowing the value of pi." It's a simple question of circling the pool with a tape measure. Could it be that Solomon -- builder of one of the architectural wonders of the ancient world, the Temple -- had a tape measure that was off by three feet?

Obviously, as the commentaries explain, the verse is offering an approximation. There are many such instances where the Torah uses approximate numbers. Just one example: When the Torah tallies the members of each of the 12 tribes (Numbers 1:20-46), each tribe's population is rounded to the nearest 50.

Why does the Torah give approximations? To offer us relevant information without burdening us with details, details often dealt with in the Oral Torah. In the case of "Solomon's Pool," the approximation teaches us that in Jewish legal matters relating to construction, we may use this 1 to 3 ratio as an approximation regarding rabbinical law.

Besides, there is no number to express the value of "pi." (That's why it's called "pi" and not written as a number.) No matter how specific the verse would be, you could always ask, "why wasn't it more specific?" That is, if the verse had said the pool was 31.4 units around, you could say, "that's wrong, it was really 31.415..." and so on.

In conclusion, the Torah sometimes approximates, and in the case of "pi" approximation is mandatory, and none of this shows anything about the Torah's authorship, Moses' ability to count or Solomon's ability to wield a tape measure!

A fascinating footnote for the mathematically-minded: The Vilna Gaon enlightens us to the fact that the value of "pi," 3.1415, is hinted in this verse. In Hebrew, each letter has a number associated with it. In the above verse, the word "circumference"(kav) is written one way "kuf vav heh" which equals 111 but it is pronounced a slightly different way "kuf vav" which equals 106. (That is, there is a stated value and an actual value.) The ratio of these two numbers equals the ratio of 3 ("pi" as stated by the verse) 3.1415 (the actual value of "pi" to the 10,000th). [ie. (111 / 106) x 3 = 3.1415]

Sources:
• Rambam, Commentary on the Mishna
• Aruch Hashulchan Orach Chaim 363:22
• See Eruvin 14a

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