Vol 79 (1998)

George M. Hollenback, «The Value of Pi and the Circumference of the "Molten Sea" in 3 Kingdoms 7,10», Vol. 79 (1998) 409-412

The dimensions of the "molten sea", the huge vessel fabricated for King Solomon’s temple, are given in 1 Kgs 7,23.26 (MT) and 3 Kingdoms 7,10.12 (LXX). All measurements of the MT correspond exactly to those of the LXX except one, the circumference. The MT gives "thirty cubits" and the LXX "thirty-three cubits". It seems probable that the MT used the value attributed to pi by the Old Babylonian (pi = 3), whereas the LXX may have known the more accurate value discovered by Archimedes and presumably known in Alexandria (pi = approximately 3 1/7).

30 cubit inside circumference at face value may lie in the text’s statement that a line (hwq, "measuring line") of 30 cubits measured the circumference of the sea. A measuring line can easily be stretched around the outside of a round vessel, but not the inside of a round vessel. Sufficiently increasing the length of the 30 cubit circumference converts it from an inside measurement to an outside measurement, thereby making it possible to stretch a measuring line around it. After a few trial divisions by 3 1/7 of tentative circumference measurements greater than 30 cubits, the LXX translator/editor would have hit upon this "perfect" measurement of 33 cubits. He furthermore could have rationalized his actions by supposing that he was emending a corrupt text: Perhaps a careless copyist, intending to transcribe an original circumference of "thirty and three" cubits, had omitted the "and three" and had simply written "thirty" 6.

A possible objection could be raised against this analysis on the grounds that there are significant differences between the material in Kings and Kingdoms, including other discrepancies in measurement. In fact, one of these discrepancies involves another circumferential measurement – that of the large twin columns flanking the temple entrance. 1 Kgs 7,15 gives the measurement as 12 cubits, but 3 Kingdoms 7,3 gives it as 14 cubits. The implication is that the LXX translator/editor could have been working from a Vorlage which perhaps did give the circumference of the sea as 33 cubits. The 33 cubit circumferential measurement is more than just a variant of a particular dimension, however. Unlike the circumferential measurements of the columns, the circumferential measurement of the sea is accompanied by a given diameter – and whenever a given diameter appears in conjunction with a given circumference, there is a definite possibility that an implicit statement about pi is being made.

If the author of the Vorlage intended the measurements to describe the same circle (e.g., maximum outside dimensions), he would be implying a pi value of 33 divided by 10 = 3.3, a value even less accurate than the old Babylonian value of 3 and a value nowhere else attested in antiquity 7. If, however, he intended the measurements to describe the two separate circles comprising inside and outside dimensions, the measurements would still reflect the old Babylonian value of 3: Dividing the 33 cubit circumference by 3 gives an outside diameter of 11 cubits, indicating a brim width of exactly one-half cubit or one span. Then again, there is no reason why such a Vorlage could not have given the same 30 cubit circumference as the MT. After all, this is the figure that repeatedly shows up in other sources