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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 11:43 AM

Franz's muddled transliteration and correct final unit fraction series:

"The arithmetical operations in the Rhind Mathematical Papyrus are crystal clear. They form the apparent level. They are what a beginner had to learn. If he could perform them in his sleep (as we say in Switzerland) he was told about the higher levels of a problem. Here is another 'silly' interpretation of mine, RMP 32 on the advanced level, offering another piece of numerical wit, and one more theorem:

RMP 32 - a magic parallelepiped

Ahmes divides 2 by 1 '3 '4 and obtains 1 '6 '12 '114 '228.

Imagine a right parallelepiped of these measurements:

height 2 units
length 1 '3 '4 units
width 1 '6 '12 '114 '228 units "

has been correctly transliterated by Peet, Gillings, and other scholars as an algebra problem that solved:

x + (1/3 + 1/4)x = 2

by considering

x + ((4 + 3)/12)x = 2

(19/12)x = 2

x = (2x 12/19) = 24/19

x = 1 + 5/19

Many scholars diverted attention due to their lack of understanding of the scribal conversion of 5/19 which reported

1 + 1/6 + 1/12 + 1/114 + 1/228

It is now clear that Ahmes converted

5/19 x (6/6) = 30/114 = (19 + 1)/114 + 10/114

5/57 x (12/12) = 60/684 = (57 + 3)/684 = 1/12 + 1/228

and recorded

1 + 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
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12/18/11 Milo Gardner
12/19/11 Milo Gardner
12/20/11 Milo Gardner
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1/3/12 Milo Gardner
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8/31/12 Milo Gardner