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King Solomon's Pi
Written August 19, 2003
Revised August 2008 and January 2017

 

King Solomon fetched from Tyre Hiram, the son of a widow of the tribe of Naphtali.  His father, a native of Tyre, had been a worker in bronze, and he himself was a man of great skill and ingenuity, versed in every kind of craftsmanship in bronze.  After he came to King Solomon, Hiram carried out all his works.

He made the Sea of cast metal; it was round in shape, the diameter from rim to rim being ten cubits; it stood five cubits high, and it took a line thirty cubits long to go round it.

I Kings 7:13-14, 23 (Revised English Bible)


The Sea was a very large vessel.  Translating its dimensions to modern units, it was comparable to an above-ground swimming pool:  about 16 feet across and 8 feet high, containing about 20,000 gallons.  In Asimov's Guide to the Bible, Isaac Asimov remarked:

“The exact function of the ‘molten Sea’ is not stated, though it seems most likely that it was a container for water used in the various rituals.

“The interesting point is that its upper rim seems to be circular in shape with a diameter of ten cubits and a circumference of thirty cubits.  This is impossible, for the ratio of the circumference to the diameter (a ratio called ‘pi’ by mathematicians) is given here as 30/10 or 3, whereas the real value of pi is an unending decimal which begins 3.14159 . . .  If the molten Sea were really ten cubits in diameter, it would have to be just under thirty-one and a half cubits in circumference.

“The explanation is, of course, that the Biblical writers were not mathematicians or even interested in mathematics and were merely giving approximate figures.  Still, to those who are obsessed with the notion that every word in the Bible is infallible (and who know a little mathematics) it is bound to come as a shock to be told that the Bible says that the value of pi is 3.”


So in states where fundamentalism rules, will Mississippi math books and Texas textbooks have to be rewritten to accommodate this biblically correct value?

Like Asimov, I have little patience with those who claim that the Bible is infallible, as it contradicts itself in many places.  For some of those, see my Bible Quiz.

However, in this case, the scripture is not necessarily incorrect in its dimensions of the Sea.  It's possible to configure Hiram's great casting in ways that would accurately agree with the Biblical numbers.

 

Configuration 1.    The vessel was “round,” but that doesn't necessarily mean it was circular.  It could have been elliptical, or perhaps oval like this plan.

The layout consists of two semicircles with diameters of 8.76 cubits, separated by a  rectangle 1.24 cubits wide.

At its widest point, A to B, this Sea measures 8.76 + 1.24 = 10.00 cubits from brim to brim.  Its circumference is (8.76 x pi) + 1.24 + 1.24 = 30.00 cubits.

However, the chances are that the Sea was indeed circular.  The scripture implies that it was fully symmetrical.

All round the Sea on the outside under its rim, completely surrounding the thirty cubits of its circumference, were two rows of gourds, cast in one piece with the Sea itself.

It was mounted on twelve oxen, three facing north, three west, three south, and three east, their hindquarters turned inwards; the Sea rested on top of them.

Its thickness was a hand's breadth.  Its rim was made like that of a cup, shaped like the calyx of a lily.  It held two thousand bath.

I Kings 7:24-26

So the oval plan is probably not the best solution to the problem.

 

Configuration 2.    Suppose the shape was not a perfectly round circle but rather an approximation consisting of straight lines. 

For example, the Temple’s ancient site is now occupied by the Dome of the Rock (right).  Despite its round dome, the base of the building is an octagon.

We're told the Sea was “cast in one piece,” but it would have been easier to assemble it from flat vertical slabs.

In the early 1960s, when I used a plastic construction set to build a model of the Temple (below), I included a 20-cubit square altar in front of it.  However, my rectangular pieces didn’t lend themselves to depicting a 10-cubit round Sea.

Now another plastic model has been built by another teenager named Thomas, using Legos.

He solved the problem by making the Sea not round but octagonal.  It’s mounted on a dozen Lego cattle in the lower left of this photo.  (A larger photo is here.)

There’s precedent in the real world for a not-perfectly-round Sea.

In Mormon temples there are often baptisteries modeled after Solomon’s, including the twelve oxen.  Many of these baptismal fonts are perfectly circular, but others are polygonal, often with ten sides like this one. 

I experimented with different numbers of sides and discovered that the magic number is six.

Behold!  A hexagonal vessel has a diameter of 10 cubits (5+5), and it takes a line 30 cubits long (6x5) to go around it, exactly as the Bible says!

 

Configuration 3.    Nevertheless, I think the Bible is probably describing a circular Sea.  But let us consider it in three dimensions.  We know that it had a rim, so it was somewhat narrower just under the rim.  It could have had its circumference measured not around its flared rim but at a lower point where it was slimmer.

For an extreme example, consider swimmer Michael Phelps.  Measure his diameter across his 79-inch wingspan, and his circumference around his 32-inch waist, and you'll conclude that pi must be 0.40506.

Solomon's Sea could easily have measured 10.00 cubits from brim to brim, yet have been only 9.55 cubits wide at the waist, where “it took a line thirty cubits long to go round it” because 9.55 x pi = 30.00.

And would that not be the natural way to measure the circumference, by running a measuring cord around the Sea at its narrowest point?

H. Peter Aleff agrees in this article on his Recovered Science website.  "The surveyors would hardly have tried to stretch their measuring rope around the proud outside of that rim where it would never stay up.  The only practical way to measure such a flared vessel is to stretch the rope around the body below that rim.  . . . The circumference and diameter reported were thus not for the same circle, and deducing an ancient pi from these unrelated dimensions would be about as valid as trying to deduce your birth date from your phone number."

Aleff then uses the Bible's dimensions for thickness, height, and volume to deduce that the shape of the Sea had to be a cylinder, not the rounded pot I sketched above.  He even calculates the exact shape of the rim, like that of a cup, shaped like the calyx of a lily, as shown in drawings like these.

The ancients were not mathematical illiterates.  They were heirs to the even-more-ancient designers of the Pyramids.  And the Bible they wrote is vindicated!  It does not require the value of pi to be 3.

  

TBT

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