Posted by: BibleScienceGuy | August 11, 2021

π (Pi) in the Bible

(4 Minute Read. 11Aug2021)

Mosaic outside Mathematics Building
at the Technical University of Berlin.

Does the Bible say incorrectly that
π = 3?

This is a common claim and criticism of the Bible which I will address in this article.

π

The mathematical constant represented by the Greek letter Pi (π) is the ratio of a circle’s circumference to its diameter: C = πD.
π also appears in the formula for the area A of a circle of radius R: A = πR2.
Some people dispute this last formula, believing that pies are round.

The number π turns up in numerous formulas throughout mathematics and physics. The patterns are elegant and intriguing. Here are a couple of surprising ones:
π/4 = 1/1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + . . . (Leibnitz’s Formula)
π2/6 = 1/12 + 1/22 + 1/32 + 1/42 + 1/52 + . . . (Euler’s Formula)

π is an irrational number. Irrational means that it is not the ratio of two integers. Its decimal expansion never ends and never endlessly repeats. The approximate value of π to 50 decimals is
3.14159265358979323846264338327950288419716939937510.

Figuring that 50 decimal digits of π will be as much as I will ever need, I have memorized this 50-decimal crude approximation to π using these groupings of digits to make it easy to remember:
3.1415926 535 8979 323 84 626 43383 27950 2884 1971 69399 37510.
Maybe the next time I write about π I will have 100 digits memorized, just for fun.

Rajveer Meena reciting 70,000 digits of π

According to Guinness World Records, the current record for memorizing digits of π is 70,000 digits by Rajveer Meena of India in March 2015. He wore a blindfold throughout his 10-hour recitation of the digits. I do not plan to challenge his record.

Memorizing digits of π is good exercise for your brain, just as memorizing Bible verses is. For help remembering numbers, read my article Remembering Numbers.

The earliest known post-Flood calculation of π was by the Greek mathematician Archimedes (287–212 BC). Ever since, mathematicians have been computing more and more decimal digits of π. The current record is 50 trillion (50,000,000,000,000) digits by Timothy Mullican in 2020.

Mathematicians even have methods for calculating specific digits of π without having to calculate all the preceding digits. For example, the quadrillionth (1,000,000,000,000,000th) decimal digit of π is 0.

π in the Bible

The claim that the Bible teaches that π = 3 is based on this Old Testament Bible passage describing a large round basin in Solomon’s Temple:
Now he [Hiram] made the sea of cast metal ten cubits from brim to brim, circular in form, and its height was five cubits, and thirty cubits in circumference. And under its brim gourds went around encircling it ten to a cubit, completely surrounding the sea; the gourds were in two rows, cast with the rest. It stood on twelve oxen, three facing north, three facing west, three facing south, and three facing east; and the sea was set on top of them, and all their rear parts turned inward. And it was a hand breadth thick, and its brim was made like the brim of a cup, as a lily blossom; it could hold two thousand baths. (1 Kings 7:23-26. Cf. 2 Chronicles 4:2-5)

The claim is that the Bible says the circumference C of a circle is 30 and the diameter D is 10, so the Bible is saying that π = C/D = 30/10 = 3.

First, the Bible never says that the value of π is 3. It never says the ratio of the circumference of a circle to its diameter is three. What it does do is give measurements of a large round basin. The metal basin was cast by hand and was not expected to be a mathematically precise circle. Plus, measurements are almost never exact. They are almost always approximate. If you measured the circumference C and diameter D of a round swimming pool in your neighborhood, the C/D ratio may or may not be close to 3 because of measurement variation. If you reported a 30-foot circumference and a 10-foot diameter, that does not mean you are announcing that π is 3.

Since π is an irrational number, any measurement of the circumference C and diameter D of a circle will necessarily yield only an approximate value C/D for π.

Since we know the value of π to be 3.1415926. . ., the 30-cubit and 10-cubit measurements must be measurements to the nearest integer. Dividing 30 by 10, we get an approximate value for π of 3. This is certainly a valid approximation for π. To the nearest integer, π is 3. This approximation of 3 for π is only 4.5% off the true value of π.

I myself have used 3 for π many times in doing approximate mental calculations — like evaluating and comparing pizza prices and pie prices, among other things.

The basin’s diameter could have been anywhere from 9.5 to 10.5 cubits and then rounded to the nearest integer to report 10 cubits. Likewise, the circumference could have been anywhere from 29.5 to 30.5 cubits and then rounded to the nearest integer to report 30 cubits. If the basin diameter was measured as 9.6 cubits and the circumference as 30.2 cubits, these values would round to 10 and 30 cubits respectively. Plus, C/D = 30.2/9.6 = 3.14583 which differs from π by only about a tenth of a percent.

No matter what values 1 Kings 7:23 reported for the circumference C and diameter D of the Temple Basin, C/D would only be an approximation to π. It would never be exactly π. No one knows or ever will know the exact decimal value of π. It is impossible for the Bible or any book to give an exact decimal value for π.

Solomon’s Temple Basin
(1890 Holman Bible image)

Second, the basin was a “hand breadth” thick (about four inches), and its brim flared out like a lily. The record in 1 Kings 7 does not specify whether the diameter measurement was the inner or outer diameter of the basin, nor whether the circumference measurement was the inner or outer circumference.

If the diameter measurement was the outer diameter (brim to brim) and the circumference was the outer circumference via a measuring cord pulled tight around the basin right underneath the flared brim, then the diameter and circumference measurements are of two different circles.

If we assume the flare of the brim was about the thickness of the basin (4 inches), then adjusting the diameter to match the measured circumference we have (using 1 cubit = 18 inches):
Diameter D = 10 cubits – 2 hand breadths = 10 x 18 in – 8 in = 172 in
Circumference C = 30 cubits = 30 x 18 in = 540 in
C/D = 540/172 = 3.1395 ~ 3.14
which approximates π to two decimals.

In conclusion, the Bible does not say that π equals 3, and it does not skew geometry with respect to the value of π. Those who allege an inaccuracy are wrong, as they misinterpret and fail to take account of all the data. Thus the criticism that there is a mathematical error in the Bible regarding π is totally without merit.

Questions to Ponder

1. What apparent error or contradiction in the Bible concerns you the most? Have you researched scholarly work on the issue?
2. Is your heart and mind open to the authority of the Great Creator?

Share your thoughts on these questions in the comments below. It could encourage or help another reader.

For Christ and His Kingdom. Soli Deo Gloria. Alere Flammam Veritatis.

Read the prequel:
Ramanujan & Hardy

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©William T. Pelletier, Ph.D.
“contending earnestly for the faith”
“destroying speculations against the knowledge of God”
“for the defense of the gospel”
(Jude 1:3; 2 Cor 10:5; Phil 1:16)
Wednesday August 11, 2021 A.D.

The sum of Thy word is truth, and every one of Thy righteous ordinances is everlasting. (Psalms 119:160)

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Responses

  1. I always love a good response to Biblical criticisms.

    Like


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