PI in the Bible

In 1 Kings 7:23 we read,

He [Solomon] made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim [diameter = 10] and five cubits high. It took a line of thirty cubits to measure around it. [circumference = 30]

Since circumference = PI x diameter as any elementary geometry book will tell you, therefore the Bible "seemingly" tells us that PI = 3. Since "this is obviously false, therefore the Bible cannot be from God..." is how some people like to reason.

But obviously the wisdom of God is greater than the wisdom of man:

In this verse the word for "circumference" (QaVa in Hebrew) is written with an extra letter (qavah).

Since in Hebrew all letters are also numbers, we can take the ratio of (the gematriacal value of) the unusual word form (qof, vaf, he ) to the regular word form (qof, vaf). Given that Qof = 100, Vaf = 6 and He = 5 we find that

( 111 / 106 ) = ( 3.14150943... / 3 )

The real value: PI = 3.1415926...

The difference between 3 x 111/106 and PI is 0.0000832 which is only an error of 0.00026%.

It is interesting to compare the "Solomonic" approximation of PI with the approximations used by the Babylonians and Egyptians.

PI = 3.1415926... Error Babylon : 3 1/8 = 25/8 = 3.125 0.0165926 Egypt : 3 13/81 = 256/81 = 3.16049382... 0.0189012 "Solomon": 333/106 = 3.14150943... 0.0000832

Since the ancient Egyptian or Babylonian approximations are much older than the time of Solomon it might be interesting find out what the usually used approximation of PI was at that time (Solomon was King around 1000 B.C.) in this or other parts of the world. Any helpful information on this question would be very much appreciated.

The "sound exegesis" answer: The Bible is not a scientific text book (though sometimes it makes scientific statements) and this specific passage wasn't intended to reveal the value of PI but to give a description of what the temple and its "furnishing" objects looked like. But given that the value "3" is within less than 5% error compared to the real value of PI = 3.14159... this is an acceptable approximation, even though "31 cubits" length would have been the (correctly rounded) answer that we might have expected. But who knows what "rounding" entailed in these days. And in a certain sense "30" is a "rounder" number than "31". And these last remarks are made all under the assumption that this above mentioned astonishing approximation is NOT intended.

Taking into account further information a few verses later, provides us with yet another way of understanding the text. In 1 Kings 7:26 we read about this metal pool:

It was a handbreadth in thickness, and its rim was like the rim of a cup,

like a lily blossom. It held two thousand baths.

We can imagine this to look somewhat like the following sketch:

`\ /' d = the measured diameter between | | the extreme points of the rim | | | | but circumference is measured below | | the rim at the actually smaller | | diameter c \_________________________/ >--------------d----------------< |/'

Given this information and assuming that exact numbers are given in Biblical text we could even calculate the width of the rim, if we want to... [that is a home work problem for the interested reader].

The above is a mainly a summary of ideas found in a paper by Shlomo Edward G.Belaga which is available in LaTeX format or Postscript format in Boaz Tsaban's Rabbinical Math section.

The Bible and the Value of "Pi" has a further observation.

Pi through the ages and Squaring the circle (History of Mathematics)

A fancier version of this paper (with Hebrew letters)

Numerical features in different scriptures