Hermione wrote :
"This, I'm afraid, is a glaring example of a straw man argument. What's been said on innumerable threads is that there is nothing to suggest that the AEs actually recognized that the fraction 3 1/7 or 22/7 was also the ratio of the relationship between a circle's diameter and circumference. To them, it was just a fraction."
Actually, 22/7 is the ratio of circumference to diameter. In any event, I am surprised by the certainty with which you make your statement. As I mentioned in a recent post on another thread, it is interesting - if not suggestive - to note that if one makes the diameter of a circle equal to a royal cubit in length (i.e., 28 fingers), then the circumference of that circle will be, upon empirical measurement, all but indistinguishable from 88 fingers in length. In light of the extremely limited surviving written record, I find it unduly hasty to categorically assert that this correlation would not have been discovered.
I believe that all we can correctly say at this time is that they had the direct means (i.e., a conveniently demarcated 28 unit measuring rod) and the intelligence to have easily made this discovery, but we have no written record that they actually did so.
In addition, let me add that had they discovered the 88 to 28 correlation, I believe that they would have not seen this in terms of what we now call "Pi", but rather they would have seen things in terms of a square with 22 unit sides as having the same perimeter as a 28 unit diameter circle. In other words, the correlation of concern would have been 11 to 14. Does this relationship sound familiar to anyone?
Best,
Lee Cooper