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Re: Ariadne's thread
Posted:
Dec 24, 2011 3:12 AM
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RMP 40
100 loaves of bread are distributed as follows: 3 men
obtain 23 "3 '7 loaves each, and 2 men receive 14 '4 '28
loaves each. Let me proceed in the same way as before:
23 "3 '7 minus 14 '4 '28 equals 9 '2 '42
'42 x 1000 minus '70 x 1000 equals '105 x 1000
'42 minus '70 equals '105
'6 minus '10 equals '15
'6 equals '10 plus '15
This equation is part of another number pattern:
'2 equals '6 '1x3
'6 equals '10 '3x5
'10 equals '14 '5x7
'14 equals '18 '7x9
'18 equals '22 '9x11
...
By recursion you get the infinite series
'2 equals '1x3 '3x5 '5x7 '7x9 '9x11 '11x13 '13x15 ...
of the subseries
'1x3 '5x7 '9x11 '13x15 '17x19 ... = pi/8
'3x5 '7x9 '11x13 '15x17 '19x21 ... = '2 minus pi/8
that can be given as 'stairways':
'1x3 '16
'1x3 '5x7 '32
'1x3 '5x7 '9x11 '48
'1x3 '5x7 '9x11 '13x15 '64
...
'3x5 '24
'3x5 '7x9 '40
'3x5 '7x9 '11x13 ?56
'3x5 '7x9 '11x13 '15x17 '72
...
For pi we get
8 times '1x3 '16
8 times '1x3 '5x7 '32
8 times '1x3 '5x7 '9x11 '48
8 times '1x3 '5x7 '9x11 '13x15 '64
...
4 minus 8 times '3x5 '24
4 minus 8 times '3x5 '7x9 '40
4 minus 8 times '3x5 '7x9 '11x13 '56
4 minus 8 times '3x5 '7x9 '11x13 '15x17 '72
...
The average of the lines number four
8 times '3 '35 '99 '64
4 minus 8 times '15 '63 '143 '255 '72
is practically '120 of 377, a value from the most
important pi sequence
3/1 (plus 22/7) 25/8 47/15 69/22 ... 377/120
The Egyptians calculated the circle on the basis of the
Sacred Triangle 3-4-5, they used pi sequences, and they
created at least the mathematical tool for the above
pi series.
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