Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Egypttian and Greek sqare root
Replies: 9   Last Post: Dec 13, 2012 8:17 PM

 Messages: [ Previous | Next ]
 Milo Gardner Posts: 1,105 Registered: 12/3/04
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

Date Subject Author
11/27/12 Milo Gardner
11/30/12 Milo Gardner
11/30/12 Milo Gardner
12/1/12 Milo Gardner
12/2/12 Milo Gardner
12/3/12 Milo Gardner
12/3/12 Milo Gardner
12/7/12 Milo Gardner
12/8/12 Milo Gardner
12/13/12 Milo Gardner