Date: Dec 8, 2012 10:05 PM
Author: Milo Gardner
Subject: Re: Egyptian and Greek sqare root
D. CONCLUSION: Finite square root was commonly written in vulgar and unit fractions from 2050 BCE to 1454 CE. The 3,500 year life of the method estimated irrational roots of numbers like 114 by easy 2-steps and 3-steps.

Step 1. guess#1 (10 + 14/20)^2 = (10 + 7/10)^2 = 100 + 7 + 7 + 49/100, 49/100 is large error

Step 2. guess#2 (10 + 2/3)^2 = 100 + 6 2/3 + 6 2/3 + 4/9 = 113 +( 3/9 +4/9) = 113 + 7/9, an acceptable 2/9 error

Step 3. reduce 2/9, divide 2/9 by 2(10 + 2/3) = 2/9(3/64) = 1/96

best estimate: square root of 114: (10 + 2/3 + 1/96)^2 contains a(1/96)^2

It should be noted that the arrival of the base 10 decimal system in 1585 AD, and other European forces formally ended the daily use of the method. The method was faintly reported for the next 400 year. Scholars and math educators may find a small niche for this once dominate method in European, USA and other math classrooms.