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Re: Egyptian fraction math only used quotient and remainder statements
Posted:
Dec 22, 2011 10:07 AM
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RMP 35- 38, 66 solved hekat problems that defined a small hekat unity as 320 ro.
That meant small hekat unity 320/320 problems and answers can be translated into modern arithmetic that multiplied one hekat, or portions thereof, by 1/n.
RMP 38 was particularly interesting. The problem multiplied
320 ro by 7/22 and obtained 101 + 9/11
written in unit fraction series.
Ahmes proved the accuracy of his unit fraction answer by multiplying
by 22/7 that obtained the initial value: 320 ro
In contrast, RMP 80, 81, 82 and 83 problems used a large hekat unity 64/64 over 60 times.
The Akhmim Wooden Tablet established the large hekat unity tradition that multiplied 64/64 by 3, 7, 10, 11 and 13. Daressy tried to explain these unit fraction answers in 1906, and failed to prove the 11 and 13 cases were exact.
The AWT scribe proved each unit fraction answer by multiply by 1/3, 1/7, 1/10, 1/11 and 1/13, respectively, that created a tradition dated to the beginning of the Middle Kingdom, facts published by Hana Vymazolva in 2001, and thereby corrected aspects of Daressy's 1906 1/11 and 1/13 issues.
Ahmes was equally at ease using large and small hekat unities, depending upon the problem being discussed.
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