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Topic: Egyptian fraction math only used quotient and remainder statements
Replies: 18   Last Post: Aug 31, 2012 9:23 AM

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 Milo Gardner Posts: 1,105 Registered: 12/3/04
Re: Egyptian fraction math only used quotient and remainder statements
Posted: Dec 17, 2011 1:16 PM

As discussed in

http://ahmespapyrus.blogspot.com/

RMP 32 solved the algebraic equation by reporting

x + x/3 + x/4 = 2

translated into modern algebra by

(19/12)x = 2

Ahmes algebra written as the EMLR student would have recorded

x = 24/19 = 1 + 5/19(4/4) = 1 + 20/76 = 1 + (19 + 1)/76 = 1 + 1/4 + 1/76

Ahmes discussed x + x/3 + x/4 = 2, and considered

(144 + 144/3 + 1449/4)x = 288

x = 1 + 1/6 + 1/12+ 1/114 + 1/288

recorded in shorthand notes:

1. 1 + 1/3 + 1/2 to get 2

\2/3 1 1/3 152
\1/3 1/2 1/16 76
\1/6 1/4 1/72 38
\1/12 1/8 1/144 19
\1/228 1/144 1
\1/114 1/72 2

a complete scribal longhand answer was not recorded by Ahmes, however, it is clear that Ahmes algebra scaled

x = 1 + 5/19 = 1 + 30/288 = 1 + (38 + 19 + 2 +1)/288 = 1 + 1/6 + 1/12 + 1/114 + 1/288

Date Subject Author
12/15/11 Milo Gardner
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