
Re: Egypttian and Greek sqare root
Posted:
Nov 30, 2012 6:22 PM


It should be stressed that the scribal method for taking the 200 BCE square root of 164 began that estimated
(12 + 4/5)^2 , a step that was short by E1 = 4/25
A second step added a unit fraction term that required the scribe to scale 4/5 by 24/24 such that:
4/5(24/24) = 96/120 = (80 +8 + 5 + 3)/120 = 2/3 + 1/15 + 1/24 + 1/40
The scribal step replaced 1/40 by 1/32 and thereby eliminated the E1 shortfall ... BUT added a smaller irrational error E2 = (1/160)^2

