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Re: Ariadne's thread
Posted:
Dec 23, 2011 3:51 AM
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RMP 39
100 loaves of bread are distributed among ten men. 50
loaves are given to 5 men. Each man obtains 12 '2 loaves.
The remaining 50 loaves are given to 6 men. Each man
receives 8 '3 loaves. Now Ahmes calculates the difference
12 '2 minus 8 '3 equals 4 '6
Let me continue as follows:
'2 x 25 minus '3 x 25 equals '6 x 25
'2 minus '3 equals '6
'2 equals '3 plus '6
This equation belongs to a stairway:
'2 = '2
'2 = '1x3 '6
'2 = '1x3 '3x5 '10
'2 = '1x3 '3x5 '5x7 '14
'2 = '1x3 '3x5 '5x7 '7x9 '18
'2 = '1x3 '3x5 '5x7 '7x9 '9x11 '22
...
'2 = '1x3 '3x5 '5x7 '7x9 '9x11 '11x13 '13x15 '15x17 ...
This series has an interesting subseries that can again
be rendered as a stairway:
'1x3 '5x7 '9x11 '13x15 '17x19 '21x23 ... = pi/8
'1x3 '16
'1x3 '5x7 '32
'1x3 '5x7 '9x11 '48
'1x3 '5x7 '9x11 '13x15 '64
'1x3 '5x7 '9x11 '13x15 '17x19 '80
...
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