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Re: Egypttian and Greek sqare root
Posted:
Dec 3, 2012 8:37 AM
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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?
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