PI in the Bible

By Jochen Katz

1 Kings 7:23 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, but 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 case the word for circumference = "line" ( in Hebrew)
But in this verse "line" is written with an extra letter (  ).

Since Hebrew has no digits, all letters are also numbers, we can take the ratio of (the gematriacal value of) the unusual word form (   ) to the regular word form ( ). Given that the gematrial letter values are = 100, = 6, and = 5 we find that:

++ +
5 + 6 + 100 = 111 6 + 100 = 106 111/106 = 1.0471698

False number for PI Ratio TOTAL
3 multiplied by
1.0471698 = 3.14150943...

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.

Another interesting aspect, the letters used here    are the only letters in Hebrew that will reveal this ratio with the difference between the gematriacal value of 3 letters and 2 letters. In other words this is the absolute lowest mathematical sequence in Hebrew to produce this ratio.

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:

1 Kings 7:26 It [the above mentioned metal pool] was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom. It held two thousand baths.
which we can imagine to be like:

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

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

Jochen Katz

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