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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

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.

Date Subject Author
4/29/11 Milo Gardner
4/29/11 Milo Gardner
4/30/11 Milo Gardner
5/2/11 Milo Gardner
5/1/11 Milo Gardner
5/3/11 Milo Gardner
5/4/11 Milo Gardner
5/13/11 Milo Gardner
5/13/11 Milo Gardner
5/14/11 Milo Gardner
5/14/11 Milo Gardner