Recent discussions related two recent HM posts cited base 60 inverses
computed by Babylonian scribes using several approximations. Eleanor
Robson, a Babylonian math scholar has indicated these facts for some
time now. The best that I have seen for 1/7 = 13/90, written out in
base 60 unit fractions, of course. More interesting is the paired 1/13
approximation that Babylonians wrote as 7/90.
This class of problem was child's play to Egyptians, even during the
Old Kingdom, as I am told (The EEF list provided several interesting
points on this area, over the last few days). To return to this
discussion, by 1650 BC, copying from 1850 BC, the RMP scribe wrote
2/7 = 13/91, or in unit fractions = 1/4 + 1/28
2/13 = 7/91, or in unit fractions = 1/8 + 1/52 + 1/104
as exact statements, or in a finite notation, where rational numbers
1/p, 1/pq, 2/p, 2/pq, ..., where written in exact and concise unit
fraction series.
My question to list members is, why did Babylonians not learn, or copy
from Egyptians, how to exactly compute in finite arithmetic? Stated
another way, could have Babylonian scribes exclusively remained in
the arithmetic domain of infinite series numeration because Egyptian
scribes/priests wished not to share their knowledge?
Regards to all,
Milo Gardner