28 April 1991

Pi and the Bible

Some mathematical comments are in order to add to the discussion of pi. If one takes a more analytical look at the Bible verses noted (II Chronicles 4:2-5 and I Kings 7:23-26), one will arrive at a ratio that is startlingly close to the real value of pi (3.14159+).

One fact that is overlooked in discussions of this sort is that the wall of the "sea" (bowl) was "one handbreadth" in thickness (I'm assuming that a handbreadth is about four inches and a cubit is about 18 inches, but more on this later). Taking the thickness of the walls into account, and assuming that the 10 cubit diameter was measured from the outside edge and that the 30 cubit circumference was measured along the inside edge, we compute pi thus:

    Ci = 30 cubits		inside circumference
       = 540 inches

    Do = 10 cubits		outside diameter
       = 180 inches

    T  = 4 inches		wall thickness

given the following relationships:

    Ci = pi × Di

    Di = Do - 2 × T		inside diameter

and substituting, we get:

    Ci = pi' × (Do - 2 × T)

    pi' = ------------		described value of pi
           Do - 2 × T

               540 inches
        = --------------------
           180 - 2 × 4 inches

        = 3.139534+

The difference between the described value of pi (pi') and the actual value of pi is:

             pi - pi'
    error = ---------- × 100%

             3.141592+ - 3.139534+
          = ----------------------- × 100%

          = 0.0655%

This means that, given the assumptions above, the Biblical description of pi differs from the real value of pi by less than a fifteenth of a percent, or a measuring error of about a third of an inch. Not bad for measurements done by hand. This also agrees with the description of a "circular" bowl and not some other shape (such as a hexagon) that some scholars have postulated.

Now about that assumption I mentioned ealier. Although ancient standards of measure vary widely, a cubit is generally taken to be about 18 inches, although there are different types of cubits ("common" and "royal", varying from 17 to 22 inches). A handbreadth is taken to be about 3 inches, sometimes being defined as one-sixth of a cubit. However, if we assume that the Biblical account uses measurements rounded off to the nearest whole number (something the Hebrews did a lot), we can read "one handbreadth" as "one handbreadth, give or take a bit," making it completely reasonable to use a value of four inches. It is also reasonable for us to measure along the inside as well as the outside edges, since the verses don't explain how the measuring was done.

This same argument was made around AD 150 by the Hebrew Rabbi Nehemiah in his "Mishnat ha-Middot", the earliest known Hebrew geometry text. (See "A History of Pi" by Petr Beckmann, an entertaining story of the search for pi, for more details.)

Anyway, the bottom line in this whole discussion is that pi is a ratio between abstract geometric concepts, a purely mathematical idea not derived from any physical object or manifestation. As such, it is impervious to physical laws and, by the same token, legislative laws.

As an aside, I would like to point out that I Kings and II Chronicles contain numerous discrepancies in measurements and enumerations. For example, II Chronicles 4:5 states that the sea (bowl) had a capacity of 3000 "baths" (a "bath" is about 8.5 gallons), while I Kings 7:26 states a capacity of 2000 baths. Hardly supporting evidence to the claim that the Bible decrees pi to be "exactly three," when the numbers in two seemingly identical accounts don't even agree.

David R. Tribble
Plano, TX

Copyright 1991-1998 by David R. Tribble, all rights reserved.