2018/05/03 by David Neustadter, Neustadter, David
Physics and Astronomy · #FOS: Mathematics #Historical Astronomy and Related Studies #History and Overview (math.HO)
paper · pdf · doi:10.48550/arxiv.1805.01505
openalex publication_date 2018/05/03 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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.