```Date: Oct 11, 2012 3:14 PM
Author: Milo Gardner
Subject: Re: Why study Egyptian fraction math?

MODERN TRANSLATIONS: Many 20th century translations of Middle Kingdom finite arithmetic texts have been incomplete, misleading and in error in major ways. Ahmes' actual Middle Kingdom finite notation used LCM m, a number theory concept, a fact not mentioned by scholars. Egyptian scribes scaled rational number by LCM m within (n/p)(m/m) = mn/mp to record concise unit fraction series (in a multiplication context). Egyptian scribes selected the best divisors of denominator mp (a GCD) that best summed to numerator mn by following the implicit algebraic context:a. n/p = n/p(m/m) = mn/mqexample: 4/13 = 4/13(4/4) = 16/52 = (13 + 2 + 1)/52 = 1/4 + 1/26 + 1/52with the divisors of mp often recorded in red that best summed to numerator mn created concise unit fraction series.A second algebraic context was recorded in RMP 37. The subtraction context was emulated by Arabs and Fibonacci per:b. (n/pq - 1/m)= (mn -pq)/mpexample: (4/13 - 1/4)= (16 - 13)/52 = (2 + 1)/52 = 1/26 + 1/52also meant 4/13 = 1/4 + 1/26 + 1/52
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