August 15, 2016

We normally look to the Bible for morals, religious inspiration, and history. But are you excited to learn that there’s some mathematics in there, too? 

If you’re a nerd like me, the answer is yes. It’s very exciting. Only chocolate syrup and whipped cream could make it better.

Most people’s favorite number is pi because it’s one of the only things they remember from geometry class in school. Pi is the ratio between the circumference and diameter of a circle, about 3.14159. The decimal digits actually go on forever because pi is irrational, meaning it can’t be written as a ratio of whole numbers. One book explains that:

“An almost cultlike following has arisen about pi. Web sites report its ‘sightings’, clubs meet to discuss its properties, and even a day on the calendar is set aside to celebrate it, that being March 14, which coincidentally is also Albert Einstein’s birthday.” (Pi: A Biography of the World’s Most Mysterious Number). 

The Bible refers to pi in two places. They seem to give the same number for pi. However, their wording differs slightly, by just one letter. The Vilna Gaon thought the discrepancy concealed a mystery.

The first reference to pi is in 1 Kings 7:23:

“Then he made the tank of cast metal, 10 cubits across from brim to brim, completely round; it was 5 cubits high, and it measured 30 cubits in circumference.”

The ratio of the circumference to the diameter gives pi a value of 3. Kind of close, but not very.

The second reference is in 2 Chronicles 4:2 is almost identical, but the Hebrew text omits the letter “heh” at the end of the word (qof, vav, heh) for circumference.

And there’s where the mystery arises. Using gematria, the Vilna Gaon calculated the first spelling’s value as 111 and the second as 106. Dividing 111 by 106 gives 1.0472. Multiplying the Bible’s pi value of 3 by 1.0472 gives — wait for it! — 3.1416, which is the rounded value of pi. Just as you’d expect if, as some scientists argue, “God is a mathematician.”

The Bible has some other mathematical references, but that one is the most interesting. And as long as we’re talking about the Ancient Near East, the Egyptians had a neat way to calculate the area of a circle that also gives a value of pi.

You might remember that the formula for the area of a circle is pi times the square of the radius, and that the radius is half the diameter.

Ancient Egyptians didn’t have a science of mathematics, but they had a lot of practical tricks to calculate land areas for surveying. To calculate the area of a circle, they drew a square whose sides were eight-ninths of the circle’s diameter. Then the area of the square was close enough to the area of the circle that they couldn’t detect any difference. 

And if you work it out, they had a value for pi that was, like the Bible’s, pretty darned close: 

·       The diameter of a circle is two times the radius, so each side of the square was 8/9ths times twice the radius, or 16/9ths times the radius.

·       The area of the square was 16/9ths of the radius multiplied by 16/9ths of the radius, which gives 256/81 times the radius squared.

·       And 256/81 equals 3.1605, a little off the rounded pi value of 3.1416. But as they say in Washington DC, “it’s close enough for government work.”

If the Egyptians had thought of their method as a mathematical formula, theirs was 3.1605 times the radius squared — very close to ours.

Other Biblical references to mathematics are little strained. In life, the Golden Ratio (1.618..) occurs frequently, especially in art and architecture. In the Bible, Exodus 25:10 says that God commanded Noah to build the Ark of the Covenant measuring 2.5 by 1.5 cubits, and 2.5 divided by 1.5 is 1.666. Some writers say it refers to the Golden Ratio, but unless the Vilna Gaon came up with something like he did with pi, it doesn’t look like it to me.

And the Bible just doesn’t have my favorite number, Euler’s number (2.71828..). I’ve learned to live with that little disappointment.