Date: Dec 3, 2012 8:37 AM
Author: Milo Gardner
Subject: Re: Egypttian and Greek sqare root
On Skype yesterday Bruce F. looked up the square root of 200 in a Demotic text, reported by Parker, as(14 + 1/7)^2

The (P + R)*2 form meant double 14 (Q) to 28(2Q), take the inverse 1/28 times (1/2Q) such that:

[200 - (14^2)] = 4/27 = 1/7 (R)

Hence, a construction foreman "quick and dirty" solution to the square of 200 = (14 + 1/7)^2 reported an excellent estimate.

But was 200 1/7 the best estimate available to professional scribes?

A scribe could have improved accuracy of any square root estimate to any given standard. This works through the implications that n/5(24/24), DID THIS FORM OFFER ONE OR MORE ACCEPTED STANDARDS?

Looking at the "quick and dirty" (Q.D.) aspects of 164^1/2, a scribe considered

12 + [1/24 x (164 -(12^2) ]= ((12 + 20/24)^2 =

(12 + 5/6)^ = 144 + 120/6 + 25/36) = 164, + E (Q.D.) = 25/36,

was unacceptable to the 200 BCE trained scribe.

A more accurate estimate was found

(12 + 2/3 + 1/15 + 1.24 + 1/32)^2

pretty neat... thanks Bruce

Anyone else have an example that is inconsistent with the above discussions?