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Topic: RMP # 48
Replies: 70   Last Post: Jul 23, 2010 8:57 AM

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 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Re: RMP # 48
Posted: Oct 9, 2007 3:19 AM
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Milo, the arithmetical 'body' of a problem in the RMP
is not enough for me, I need a 'soul' that brings a
calculation to life, and I find it by playing with the
given numbers.

RPM 56, 57, 58 and 59 concern pyramids. Three of them
have the sekad 5 palms 1 finger. A pyramid of this sekad
involves a 'sacred triangle': half base 3a, height 4a,
slope 5a. I call such a pyramid a 'sacred pyramid'.

The sacred pyramid of RMP 59 has a base of 12 royal
cubits and a height of 8 royal cubits. The slope
measures 10 royal cubits, and the radius of the
inscribed sphere 3 royal cubits. The diameter of
the inscribed sphere measures 6 royal cubits,
the same as half the base.

Now picture a wooden model of this pyramid: base 12
fingers (22.5 cm), height 8 fingers (15 cm), slope
10 fingers (18.75 cm). Calculate the surface of the
model. You'll get 144 plus 60 plus 60 plus 60 plus
60 square fingers, all in all 384 square fingers.
Calculate the volume of the model. You'll get 384
cubic fingers ...

For a next step you may transform the volume of this
pyramid into a sphere. It will have a diameter of
practically 9 fingers. This leads to a nice expansion
of the well known formula for the calculation of the
area of a circle into three dimensions:

A square of the side 8 and a circle of the diameter
9 have practically the same area; a sacred pyramid
of the height 8 and a sphere of the diameter 9 have
practically the same volume (implicit value for pi
in both cases 256/81).

Regards, Franz Gnaedinger

Date Subject Author
9/30/07 L. Cooper
10/1/07 Franz Gnaedinger
10/1/07 L. Cooper
10/1/07 Milo Gardner
10/1/07 L. Cooper
10/2/07 Milo Gardner
10/3/07 Milo Gardner
10/3/07 L. Cooper
10/3/07 Franz Gnaedinger
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 Milo Gardner
10/4/07 L. Cooper
10/5/07 L. Cooper
10/5/07 Milo Gardner
10/6/07 L. Cooper
10/6/07 Franz Gnaedinger
10/6/07 Milo Gardner
10/6/07 L. Cooper
10/6/07 Franz Gnaedinger
10/6/07 Milo Gardner
10/7/07 Franz Gnaedinger
10/7/07 Milo Gardner
10/7/07 Franz Gnaedinger
10/7/07 Milo Gardner
10/8/07 Franz Gnaedinger
10/8/07 Milo Gardner
10/8/07 Franz Gnaedinger
10/8/07 Milo Gardner
10/9/07 Franz Gnaedinger
10/9/07 L. Cooper
10/10/07 Franz Gnaedinger
10/11/07 Franz Gnaedinger
10/11/07 L. Cooper
10/12/07 Franz Gnaedinger
10/12/07 Franz Gnaedinger
10/12/07 L. Cooper
10/13/07 Franz Gnaedinger
10/13/07 L. Cooper
10/13/07 Franz Gnaedinger
10/15/07 Franz Gnaedinger
10/18/07 Ed Wall
10/19/07 Franz Gnaedinger
10/20/07 Milo Gardner
12/5/07 Milo Gardner
12/14/07 Franz Gnaedinger
12/14/07 Milo Gardner
12/14/07 Milo Gardner
10/11/07 Milo Gardner
10/12/07 L. Cooper
10/12/07 Milo Gardner
10/13/07 L. Cooper
7/11/10 Dioxippus
7/12/10 Milo Gardner
7/20/10 Dioxippus
7/21/10 Milo Gardner
7/21/10 Dioxippus
7/21/10 Milo Gardner
7/23/10 Dioxippus
7/23/10 Milo Gardner
10/6/07 Hossam Aboulfotouh
10/8/07 Milo Gardner
10/11/07 Hossam Aboulfotouh
10/12/07 Milo Gardner
10/13/07 Hossam Aboulfotouh
10/13/07 Hossam Aboulfotouh
10/19/07 Hossam Aboulfotouh
10/27/07 Matt Hugh

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