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Topic: Egyptian algebra, RMP 21 thru RMP 34
Replies: 10   Last Post: May 14, 2011 12:00 PM

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Milo Gardner

Posts: 1,105
Registered: 12/3/04
Re: Egyptian algebra, RMP 21 thru RMP 34
Posted: Apr 30, 2011 11:23 AM
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Ahmes solved the RMP 32 algebraic statement:

1 + x/3 + x/4 = 2

by LCM 144 and solved

144x + 144x/3 + 144x/4 = 288

144x + 48x + 36x = 288

228x = 288

x = 288/228

x = 1 + 60/228 = 1 + (57 + 3)/228 = 1 + 1/4 + 1/76

Ahmes wrote out duplication calculations of 48x and 36x
and proofs on a lower arithmetic level.

Ahmes can be fairly translated as

x = 1 + 5/19(4/4) = 1 + 20/76 = 1 + (19 + 1)/76 = 1 + 1/4 + 1/76

as the actual unit fraction answer.

footnote: Clagett's 1999 review of the arithmetic and algebraic facts and proof omitted discussions of numerators 288 and 60 and the final answer. Clagett did mention the correct denominator 228.



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