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Re: Egyptian fraction math only used quotient and remainder statements
Posted:
Dec 16, 2011 11:43 AM
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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.
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