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Re: RMP # 48
Posted:
Oct 8, 2007 10:45 AM
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"Correct method of reckoning, for grasping the meaning of things
and knowing everything that is, obscurities ... and all secrets"
Big promises at the begin of the Rhind Mathematical Papyrus,
translated by Gay Robins and Charles Shute. The opening lines
of the RMP raise curiosity, and when people read the problems
they are disappointed (happened also to Robins and Shute):
Where are all those obscurities and secrets?
I say we have to read the RMP with imagination. Take for example
problem 32. Ahmes divides 2 by 1 '3 '4 and gets 1 '6 '12 '114 '228.
Now consider these numbers edges of a parallelepiped:
height 2 cubits
length 1 '3 '4 cubits
width 1 '6 '12 '114 '228 cubits
How long are the diagonals of the volume? Simply 1 '3 '4 plus
1 '6 '12 '114 '228 cubits, or 1 1 plus '3 '6 plus '4 '12 plus
'114 '228 cubits or 2 '2 '3 '76 cubits. The result is _exact_,
as you like it. And there is a theorem involved:
Divide 2 by any number A and you obtain B. If a parallel-epiped
measures 2 by A by B units, the diagonals of the volume measure
exactly A plus B units.
There is evidence for this number game in RMP 32. Ahmes could
have obtained 1 '6 '12 '76 as result of his division, but he gave
the long solution 1 '6 '12 '114 '228, which allows the final
"shoot down" ...
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