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The "Jewish" or "Bible" Value of "pi"

Do the Nevi'im and the Ketuvim (sections of Jewish scripture, comprising parts of the Christian "Old Testament") really say that the value of pi is three? Not actually but, due to the social pressures to look down on all things Judeo-Christian and the perverse joy certain people get out of tormenting others, I keep receiving queries on this issue. Before we do the calculations to put this old chestnut to rest, let's lay a little groundwork.

The Quote

"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26

There is a similar description in Second Chronicles 4, verses 2 through 5.

Hiram and the Phoenicians

The Phoenicians lived in what is now Lebanon. They were the creators of "royal purple", made by boiling a particular sea snail. While they did not invent glass, they did invent glass-blowing. They invented the first alphabet, from which we derive our own Latin alphabet. And they were skilled builders and artisans who exported their talents along with their legendary wood products, the fabled "cedars of Lebanon".

Hiram was the Phoenician artisan recorded as having been hired by King Solomon to design and supervise the building of the Jewish temple. The huge bowl (or "sea") at issue was used within the temple.

The Measurements

The text refers to dimensions measured in "cubits" and "handbreadths". Back in those days, measurements were not standardized as they are now. People used seat-of-the-pants measurements. Have you ever estimated the length of a bookcase by seeing how long it was compared to your outstretched arms? And then walked over to the spot where you wanted to move the bookcase, and stood against the wall, making sure that the length you'd just measured against your own body would fit in the open space? If so, then you have used "measurements" similar to those that ancient civilizations used.

Since cubits and handbreadths are measured against a person's body, and since bodies vary, actual measurements (as opposed to "standardized" measurements) will vary from person to person. Your desk might be thirty inches tall, just like mine, but you might have bigger hands, so you might get a body-measure of only ten handbreadths. This variation is normal. Since we have no idea what Hiram's body measurements were, we'll have to approximate by using the standardized values for cubits and handbreadths.

Some Reasonable Assumptions

If this discussion of a "sea", or large bowl, had been referring to what is called an "ideal" bowl (a mathematical object, not existing in a physical sense, and having no thickness that could be felt or handled), then the text would indeed be claiming that the value of pi is three. But the text is referring to a real-world physical object, having the thick sidewalls necessary to support its own weight.

Now that you know how to measure cubits, can you see that it would be rather difficult to measure the curved surface of a bowl in cubits? Instead, a straightened rope would be used to measure the length. The rope would then have been moved to outline a circle with the desired circumference. Also, Hiram would not have just tossed some brass in the furnace and waited to see what came out. He would have designed the piece and would have given his workmen instructions.

To make a "sea" like this would likely have required a mold. The outer mold would have one dimension, and the inner mold would have another. Hiram would have given his workmen instructions regarding these measurements.

Wouldn't it be reasonable to assume that the Phoenicians, being the renowned craftsmen that they were, had discovered a "rule of thumb"? Perhaps something along the lines of, "If a bowl is made with a three-to-one ratio between the inner circumference and the outer diameter, the bowl will have a desirable wall thickness that will support its own weight"? When Egyptians and Babylonians came up with rules of thumb or accidentally discovered formulae like this, we credit them with being clever. Can't we do the same for the Phoenicians, even if they did occasionally — gasp! — cooperate with Jews?

Now that you have some background information, let's look at the actual numbers:

The Calculations

Here again is the quote being referred to:

"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26

 The bowl is said to have had a circumference of thirty cubits and a diameter of ten cubits. The diameter is said to be "from one rim to the other", so this would be the outer diameter; that is, the diameter of the outer mold used to make the bowl.

The circumference is not specified as being the inner or outer circumference, but since using the outer circumference would give us the "ideal" bowl (with no width or thickness), let's instead use the inner circumference, which also, reasonably, would have been the circumference of the mold used to form the inside of the bowl. That is, we will use the two measurements which were necessary for the casting of the piece.   Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

Using eighteen inches for one cubit, we have the following:

outer diameter: 10 cubits, or 180 inches
outer radius: 5 cubits, or 90 inches
inner circumference: 30 cubits, or 540 inches

 To find the "Jewish" or "Bible" value for pi, we need to have the inner radius. Once we have that value, we can plug it into the formula for the circumference and compare with the given circumference value of 540 inches. Since the thickness of the bowl is given as one handsbreadth, then the inner radius must be: 90 – 4 = 86 inches Let's do the calculations: inner radius:  86 inches inner circumference:  540 inches

The circumference formula is C = 2(pi)r, which gives us:

540 = 2(pi)(86)
540 = 172(pi)

Solving, we get pi540/172  =  135/43   = 3.1395348837..., or about 3.14.

Um... Isn't "3.14" the approximation we all use for pi? Perhaps those Phoenicians were fairly accurate after all.