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Topic: Ariadne's thread
Replies: 86   Last Post: Jan 28, 2013 5:19 AM

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Franz Gnaedinger

Posts: 330
Registered: 4/30/07
Re: Ariadne's thread
Posted: Dec 23, 2011 3:51 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
...


Date Subject Author
11/17/11
Read Ariadne's thread
Franz Gnaedinger
11/17/11
Read Re: Ariadne's thread
Milo Gardner
11/18/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/18/11
Read Re: Ariadne's thread
Milo Gardner
11/19/11
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Franz Gnaedinger
11/19/11
Read Re: Ariadne's thread
Milo Gardner
11/20/11
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Franz Gnaedinger
11/20/11
Read Re: Ariadne's thread
Milo Gardner
11/20/11
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Milo Gardner
11/21/11
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Franz Gnaedinger
11/22/11
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Franz Gnaedinger
11/22/11
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Milo Gardner
11/23/11
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Franz Gnaedinger
11/24/11
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Franz Gnaedinger
11/24/11
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Franz Gnaedinger
11/24/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/24/11
Read Re: Ariadne's thread
Milo Gardner
11/25/11
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Franz Gnaedinger
11/26/11
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Franz Gnaedinger
12/2/11
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Franz Gnaedinger
12/2/11
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Milo Gardner
12/3/11
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Franz Gnaedinger
12/4/11
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Franz Gnaedinger
12/4/11
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Milo Gardner
12/5/11
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Franz Gnaedinger
12/5/11
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Milo Gardner
12/7/11
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Franz Gnaedinger
12/8/11
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Milo Gardner
12/10/11
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Franz Gnaedinger
12/12/11
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Franz Gnaedinger
12/12/11
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Milo Gardner
12/13/11
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Franz Gnaedinger
12/13/11
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Milo Gardner
12/15/11
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Franz Gnaedinger
12/15/11
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Milo Gardner
12/15/11
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Milo Gardner
12/16/11
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Franz Gnaedinger
12/16/11
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Milo Gardner
12/18/11
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Franz Gnaedinger
12/18/11
Read Re: Ariadne's thread
Milo Gardner
12/19/11
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Franz Gnaedinger
12/20/11
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Franz Gnaedinger
12/20/11
Read Re: Ariadne's thread
Milo Gardner
12/21/11
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Franz Gnaedinger
12/22/11
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Franz Gnaedinger
12/23/11
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Franz Gnaedinger
12/24/11
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Franz Gnaedinger
12/29/11
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Franz Gnaedinger
1/2/12
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Franz Gnaedinger
1/3/12
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Milo Gardner
1/4/12
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Franz Gnaedinger
11/28/11
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Velev, Petyr
1/6/12
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Franz Gnaedinger
1/6/12
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Milo Gardner
1/9/12
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Franz Gnaedinger
1/17/12
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Franz Gnaedinger
1/19/12
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Franz Gnaedinger
1/19/12
Read Re: Ariadne's thread
Milo Gardner
1/27/12
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Franz Gnaedinger
2/10/12
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Franz Gnaedinger
2/28/12
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Franz Gnaedinger
3/2/12
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Franz Gnaedinger
3/23/12
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Franz Gnaedinger
3/24/12
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Milo Gardner
4/9/12
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Franz Gnaedinger
4/10/12
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Franz Gnaedinger
4/13/12
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Franz Gnaedinger
4/17/12
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Franz Gnaedinger
4/18/12
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Franz Gnaedinger
4/18/12
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Franz Gnaedinger
5/5/12
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Franz Gnaedinger
5/7/12
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Franz Gnaedinger
5/7/12
Read Re: Ariadne's thread
Milo Gardner
5/8/12
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Franz Gnaedinger
5/8/12
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Milo Gardner
5/8/12
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Franz Gnaedinger
5/8/12
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Franz Gnaedinger
5/9/12
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Franz Gnaedinger
5/10/12
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Franz Gnaedinger
8/14/12
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Franz Gnaedinger
1/13/13
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Franz Gnaedinger
1/19/13
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Franz Gnaedinger
1/23/13
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Franz Gnaedinger
1/23/13
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Franz Gnaedinger
1/24/13
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Franz Gnaedinger
1/26/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/28/13
Read Re: Ariadne's thread
Franz Gnaedinger

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