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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: Jan 27, 2012 3:22 AM
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RMP 48

Problem no. 48 of the Rhind Mathematical Papyrus contains
a famous drawing of a square with an inscribed octagon
(ASCII drawing adopted to the proportional font):

A a b B
h ----- c
g ----- d
D f e C

Square ABCD -- irregular octagon abcdefgh

A-B = B-C = C-D = D-A = 9 royal cubits

A-a = a-b = b-B = B-c = ... = g-h = h-A = 3 royal cubits

grid 3+3+3 by 3+3+3 royal cubits

area square 9x9 = 81 square cubits

area octagon 9x9 - 2x3x3 = 63 square cubits

A circle inscribed in the square would have about the same
area as the octagon. This yields the value 3 '9 for pi:

'4 x 9 rc x 9 rc x 3 '9 = 63 square cubits

63 square cubits are about 8 by 8 royal cubits. From this
we derive a well known formula: if the diameter of a circle
measures 9 units and if the side of a square measures
8 units the circle and the square have roughly the same
area. This formula yields '81 of 256 for pi, or nearly
'6 of 19 or 3 '6, according to a crosswise multiplication:

256 x 6 = 1536 --- 81 x 19 = 1539

So we found the values 3 '9 and 3 '6. The equally simple
values in between are 3 '8 and 3 '7. These values are part
of the first pi sequence

4/1 (plus 3/1) 7/2 10/3 13/4 16/5 * 19/6 22/7 25/8 28/9 *


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