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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 16, 2011 3:07 PM

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.

Date Subject Author
12/15/11 Milo Gardner
12/16/11 Milo Gardner
12/16/11 Milo Gardner
12/16/11 Milo Gardner
12/17/11 Milo Gardner
12/17/11 Milo Gardner
12/18/11 Milo Gardner
12/19/11 Milo Gardner
12/20/11 Milo Gardner
12/21/11 Milo Gardner
12/22/11 Milo Gardner
12/23/11 Milo Gardner
1/3/12 Milo Gardner
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1/6/12 Milo Gardner
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1/19/12 Milo Gardner
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8/31/12 Milo Gardner