The Jewish or Bible Value of Pi
Parsha Pages | March 21, 2025
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The Jewish or Bible Value of Pi

Parsha Pages | June 27, 2025

Does the Torah really say that the value of pi is three?

Not actually. But before we present the calculations, 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 (Haftorah Parshas VaYakhel)

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. While they did not invent glass, they did invent glass-blowing. They invented one of the first alphabet systems, from which the Latin alphabet is derived. 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 bowl ("sea") at issue was used within the temple.

The Measurements - Background

The text refers to dimensions measured in "cubits" and "handbreadths". The cubit was the length from the elbow to the tip of the outstretched fingers. It is commonly "standardized" today as being about eighteen inches (or about forty-six centimeters). To measure the length of, say, a desk in cubits, you would put your elbow at one end of the desk, with your hand outstretched toward the other end of the desk. Put the index finger of your other hand on the desk where your outstretched fingertips end, to mark the end of that cubit. Then move your cubit-arm over your index finger (which is marking the first cubit) so your elbow is now at your index finger, with your outstretched fingers still aiming at the other end of the desk. This refers to a measurement of "two cubits". Continue laying out cubits until you run out of desk, counting as you go. My desk, being seventy-two inches long, comes out to being about four and a half cubits long, as measured by my forearm.

A handbreadth is the "hand" used to measure horses. It is the width of the palm of the person doing the measuring, and is "standardized" as being four inches (or about ten centimeters). To measure, say, the height of a desk, start at the floor. Open your left hand with your palm facing you and your thumb up in the air (so it's out of the way). Rest your hand on the floor, with the back of your open hand against the desk, your palm still facing you, and your "pinkie" finger on the floor. Now open your right hand (again sticking your thumb up in the air so it's out of the way), and rest it on top of your left hand (so your right "pinkie" finger is across the top of your left index finger). This measures "two hands". Continue alternating hands up the side of your desk, counting as you go. My desk, being thirty inches tall, comes out to being about eleven handbreadths.

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.

Now that you have some background information, let's look at the 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.

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 handbreadth, 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 pi = 540 / 172 = 3.1395348837..., or about 3.14.

Um... Isn't "3.14" the approximation we all use for pi? Hmm.... I guess the Torah was fairly accurate after all.

Based on an article by Stapel, Elizabeth, "The 'Jewish' or 'Bible' Value of 'pi'"

SEE ERUVIM 14 FOR MORE INFORMATION

Does the Torah really say that the value of pi is three?

Not actually. But before we present the calculations, 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 (Haftorah Parshas VaYakhel)

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. While they did not invent glass, they did invent glass-blowing. They invented one of the first alphabet systems, from which the Latin alphabet is derived. 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 bowl ("sea") at issue was used within the temple.

The Measurements - Background

The text refers to dimensions measured in "cubits" and "handbreadths". The cubit was the length from the elbow to the tip of the outstretched fingers. It is commonly "standardized" today as being about eighteen inches (or about forty-six centimeters). To measure the length of, say, a desk in cubits, you would put your elbow at one end of the desk, with your hand outstretched toward the other end of the desk. Put the index finger of your other hand on the desk where your outstretched fingertips end, to mark the end of that cubit. Then move your cubit-arm over your index finger (which is marking the first cubit) so your elbow is now at your index finger, with your outstretched fingers still aiming at the other end of the desk. This refers to a measurement of "two cubits". Continue laying out cubits until you run out of desk, counting as you go. My desk, being seventy-two inches long, comes out to being about four and a half cubits long, as measured by my forearm.

A handbreadth is the "hand" used to measure horses. It is the width of the palm of the person doing the measuring, and is "standardized" as being four inches (or about ten centimeters). To measure, say, the height of a desk, start at the floor. Open your left hand with your palm facing you and your thumb up in the air (so it's out of the way). Rest your hand on the floor, with the back of your open hand against the desk, your palm still facing you, and your "pinkie" finger on the floor. Now open your right hand (again sticking your thumb up in the air so it's out of the way), and rest it on top of your left hand (so your right "pinkie" finger is across the top of your left index finger). This measures "two hands". Continue alternating hands up the side of your desk, counting as you go. My desk, being thirty inches tall, comes out to being about eleven handbreadths.

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.

Now that you have some background information, let's look at the 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.

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 handbreadth, 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 pi = 540 / 172 = 3.1395348837..., or about 3.14.

Um... Isn't "3.14" the approximation we all use for pi? Hmm.... I guess the Torah was fairly accurate after all.

Based on an article by Stapel, Elizabeth, "The 'Jewish' or 'Bible' Value of 'pi'"

SEE ERUVIM 14 FOR MORE INFORMATION

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Parsha Pages | March 21, 2025