  There is little known about the methods used by the ancient Babylonians and
Egyptians to arrive at their recorded estimates of the value of Pi. A
surprisingly accurate estimate of Pi was recently revealed coded within a verse
in the book of 1 Kings, the value of which suggests how it might have been
measured. The coded value is 111/106, which is a continued fraction
representation of Pi/3. This suggests that the value may have been measured
using an iterative measurement of remainders when comparing the two lengths C
(circumference of the circle) and 6R (6 times the radius). This article
describes a method that could have been used 3000 years ago to make such a
measurement, the expected measurement errors, and a computer simulation that
assesses the chances of such a method succeeding in obtaining the coded value
of 111/106. The result indicate that with the technology available at the time
the proposed measurement method would have been possible and would have had
about a 75% chance of producing the result 111/106 after a few hundred
measurements.
