
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

