Date: Oct 18, 2012 10:47 AM
Author: Milo Gardner
Subject: Re: Why study Egyptian fraction math?
MODERN TRANSLATIONS: Most 20th century transliterations and translations of Middle Kingdom arithmetic texts have been incomplete and misleading. Ahmes' actual Middle Kingdom arithmetic was finite. The arithmetic used LCM m, a number theory concept. Egyptian scribes scaled rational number by LCM m within (n/p)(m/m) = mn/mp that recorded 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/mq
example: 4/13 = 4/13(4/4) = 16/52 = (13 + 2 + 1)/52 = 1/4 + 1/26 + 1/52
with 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)/mp
example: (4/13 - 1/4)= (16 - 13)/52 = (2 + 1)/52 = 1/26 + 1/52
also meant 4/13 = 1/4 + 1/26 + 1/52