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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 18, 2011 12:30 PM

Franz imagines:

"RMP 33 - a wooden container in the shape of a cube

37 divided by 1 "3 '2 '7 equals 16 '56 '679 '776

Imagine a wooden chest in the shape of a cube. The chest plus the lid measure 41 by 41 by 41 fingers. The boards are 2 fingers strong. The inner space measures 37 by 37 by 37 fingers. How long are the diagonals of the outer faces and of the outer cube in fingers? and of the inner cube in palms?"

RMP 33 had nothing to do with a wooden container. Ahmes offered a clear number theory explanation of the algebraic problem that solved:

x + (2/3 + 1/2 + 1/7)x = 37

as RMP 31 and 32 were solved ...

as a translation, considering modern algebra

(1 + (28 + 21 + 6)/42)x = 33

(97/42)x = 37

x = 37 x (42/97) = 1554/97 = 16 + 2/97

Translating RMP 33 in an ancient sense, Ahmes could have looked up the 2/97 answer in his 2/n table or re-calculated

2/97 (56/56) = 112/5432 = (97 + 8 + 7)/5432 =

x = 16 + 1/56 + 1/679 + 1/776

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
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1/3/12 Milo Gardner
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1/6/12 Milo Gardner
1/9/12 Milo Gardner
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2/10/12 Milo Gardner
8/31/12 Milo Gardner