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Re: Egyptian fraction math only used quotient and remainder statements
Posted:
Dec 16, 2011 3:07 PM
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Ahmes discussed x + x/3 + x/4 = 2, by considering
144x + 144/3 + 144/4 = 288 by
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
hence, x = 1 + 1/6 + 1/12 + 1/114 + 1/228 was the shorthand answer, and fair translation of the above can be summarized by
1 + 5/19 = 1 + 60/288 = 1 + (38 + 19 + 2 + 1)/288 =
x = 1/6 + 1/12 + 1/114 + 1/228
Q.E.D.
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