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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 29, 2011 4:02 AM
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RMP 41

A granary in the form of a cylinder has an inner diameter
of 9 royal cubits and an inner height of 10 royal cubits.

A square of the side 8 rc and a circle of the diameter
9 rc have about the same area. So the floor of the granary
measures about 64 square cubits. Multiply this area by
the height 10 royal cubits and you will obtain a volume
of 640 cubic cubits = 960 khar = 4,800 quadruple hekat
= 19,200 hekat.

Now let us calculate the volume of the granary more exactly:

diameter 9 royal cubits or 63 palms or 252 fingers
height 10 royal cubits or 70 palms or 280 fingers

By using the value '7 of 22 for pi we obtain:

diameter 63 palms or 252 fingers
circumference 198 palms or 1386 fingers
area wall 13,860 square palms
area floor 49,896 square fingers
volume 13,970,880 cubic fingers or about 636 cubic cubits

A better result than the first one. Now, as a game for
advanced learners, we may exchange the numbers:

diameter 10 royal cubits or 70 palms or 280 fingers
height 9 royal cubits or 63 palms or 252 fingers
circumference 220 palms or 880 fingers
area wall 13,860 square palms
area floor 3,850 square palms or 61,600 square fingers
volume 15,523,200 cubic fingers or about 707 cubic cubits

The walls of the two cylinders have the same area while
their volumes maintain the ratio 9 to 10.

The diameter of another cylinder measures 15 royal cubits
and the height 6 royal cubits. The wall again has the
same area while the volume increases to 23,284,800 cubic
fingers or about 1061 cubic cubits.

A further cylinder may have a diameter of 90 royal cubits
and a height of 1 royal cubit. The area of the wall would
again be the same while the volume would increase to
about 6364 cubic cubits.

Now please consider a sequence of cylinders:

diameter 1 2 3 5 6 9 10 15 18 30 45 90 rc
height 90 45 30 18 15 10 9 6 5 3 2 1 rc

The walls have the same area while the volume increases
in a peculiar way: divide the height by any number and
the volume will increase by the same factor ... The lower
the cylinder the bigger the volume. And if the wall has
no height at all? In that case the volume would be
infinitely huge ... A pretty paradox to be discussed in
the seminary of professor Ahmes.


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
Read Re: Ariadne's thread
Franz Gnaedinger
11/26/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/2/11
Read Re: Ariadne's thread
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
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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
Read Re: Ariadne's thread
Milo Gardner
12/13/11
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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
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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
Read Re: Ariadne's thread
Franz Gnaedinger
1/3/12
Read Re: Ariadne's thread
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
Read Re: Ariadne's thread
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
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Franz Gnaedinger
4/18/12
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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
Read Re: Ariadne's thread
Franz Gnaedinger
5/10/12
Read Re: Ariadne's thread
Franz Gnaedinger
8/14/12
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Franz Gnaedinger
1/13/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/19/13
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Franz Gnaedinger
1/23/13
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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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