Wednesday, 31 January 2007

All at Sea about Pi

The otherwise excellent Penguin Dictionary of Curious and Interesting Numbers states that, “In the Old Testament, 1 Kings 7:23 implies that π is equal to 3”. Since I first read that, I have come across several internet sites that say, either implicitly or explicitly, “The Bible says π = 3, therefore it cannot be trusted.”

1 Kings 7:23-26 describes the Sea in Solomon’s temple that was used by the priests for washing: “He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it. … It was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom.”

π is the ratio of the circumference to the diameter of a circle. Here the circumference is given as 30 cubits and the diameter as 10. So the ancient Jews must have thought that π = 30/10 = 3, mustn’t they? Well, no … as I shall try to explain.

First, what is described is a very large, thick basin with a kind of lip to it, “like the rim of a cup, like a lily blossom”. It’s about 4½ metres in diameter, and about 8 centimetres thick. It’s not clear whether the rim-to-rim measurement was internal, or if it included the lip, or somewhere between. Similarly, it’s not stated whether the measurement around it included the lip or not. In fact, the “line … around it” may have been measured round the widest part of the Sea—which may not have been around rim at all: it may have bulged below the rim.

Secondly, the measurements here—and elsewhere in the description of the temple—are approximate. In fact, in the 140 or so verses in the Bible that mention cubits, most only ever refer to whole numbers of them. The remaining dozen or so refer to half-cubit measurements, but that’s the smallest fraction ever used. These are not exact measurements taken from the architect’s drawings.

So even if the measurements are both taken as referring to the same part of the rim, all we can confidently say about π from this passage is that it lies somewhere between about 29½/10½ (≈ 2.81) and 30½/9½ (≈ 3.21).


Gary Brady said...

The Bible and maths!