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Re: Ariadne's thread
Posted:
Dec 19, 2011 2:42 AM
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This here is my thread wherein I publish findings of mine
obtained with methods I reconstructed and an approach
I developed myself. Words and labels can't tear down
my work. The only way to convince me is to carry out
calculations. Pose a problem in clear and simple words,
then solve it step by step. Repeating ever the same
partitions is not calculating.
RMP 32 on the advanced level revealed what I call the
'magic parallelepiped'. Every division of 2 provides
the numbers for such a parallelepiped:
2 divided by A equals B
parallelepiped 2 by A by B
volume 4, diagonal A plus B
RMP 33 on the advanced level asked about the diagonals
of the square and cube. RMP 34 on the advanced level
returns to the 'magic parallelepiped' and uses the
theorem implied in RMP 32 for a practical purpose,
calculating a granary.
RMP 34 - an easy way to measure a granary
Let us imagine a granary in the shape of a magic
parallelepiped:
volume 500 cubic cubits / capacity 750 khars or 15,000
hekat
inner height 2 units or 10 cubits or 70 palms or 280
fingers
length x width 2 square units or 50 square cubits or
2,450 square palms or 39,200 square fingers
Here are four exact solutions, one of them provided by
Ahmes' equation 1 '2 '4 times 5 '2 '7 '14 equals 10
in RMP 34:
inner height 10 royal cubits
inner length 10 royal cubits
inner width 5 royal cubits
cubic diagonal 15 royal cubits
inner height 280 fingers (10 royal cubits or 2 units)
inner length 245 fingers (1 '2 '4 units)
inner width 160 fingers (5 '2 '7 '14 royal cubits)
cubic diagonal 405 fingers (RMP 34)
inner height 280 fingers
inner length 224 fingers
inner width 175 fingers
cubic diagonal 399 fingers
inner height 280 fingers or 70 palms
inner length 200 fingers or 50 palms
inner width 196 fingers or 49 palms
cubic diagonal 396 fingers or 99 palms
If height, length and width measure 70, 50 and 49 palms,
the cubic diagonal measures exactly 99 palms. Now
consider a very good approximation:
inner height 280 fingers
inner length 198 fingers
inner width 198 fingers
diagonal practically 396 fingers
Such a granary can be measured simply using a rope:
o-- height --o-- length --o-- width --o
o-- 10 cubits --o-- 198 fingers --o-- 198 fingers --o
o----------------------o---------------o---------------o
o----------------------o-------------------------------o
o-- 10 royal cubits --o-- 396 fingers or 99 palms --o
o-- diagonal base --o-- cubic diagonal --o
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