The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Inactive » math-history-list

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Franz Gnaedinger

Posts: 330
Registered: 4/30/07
Re: RMP # 48
Posted: Oct 9, 2007 3:19 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
Read RMP # 48
L. Cooper
10/1/07
Read Re: RMP # 48
Franz Gnaedinger
10/1/07
Read Re: RMP # 48
L. Cooper
10/1/07
Read Re: RMP # 48
Milo Gardner
10/1/07
Read Re: RMP # 48
L. Cooper
10/2/07
Read Re: RMP # 48
Milo Gardner
10/3/07
Read Re: RMP # 48
Milo Gardner
10/3/07
Read Re: RMP # 48
L. Cooper
10/3/07
Read Re: RMP # 48
Franz Gnaedinger
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
L. Cooper
10/5/07
Read Re: RMP # 48
L. Cooper
10/5/07
Read Re: RMP # 48
Milo Gardner
10/6/07
Read Re: RMP # 48
L. Cooper
10/6/07
Read Re: RMP # 48
Franz Gnaedinger
10/6/07
Read Re: RMP # 48
Milo Gardner
10/6/07
Read Re: RMP # 48
L. Cooper
10/6/07
Read Re: RMP # 48
Franz Gnaedinger
10/6/07
Read Re: RMP # 48
Milo Gardner
10/7/07
Read Re: RMP # 48
Franz Gnaedinger
10/7/07
Read Re: RMP # 48
Milo Gardner
10/7/07
Read Re: RMP # 48
Franz Gnaedinger
10/7/07
Read Re: RMP # 48
Milo Gardner
10/8/07
Read Re: RMP # 48
Franz Gnaedinger
10/8/07
Read Re: RMP # 48
Milo Gardner
10/8/07
Read Re: RMP # 48
Franz Gnaedinger
10/8/07
Read Re: RMP # 48
Milo Gardner
10/9/07
Read Re: RMP # 48
Franz Gnaedinger
10/9/07
Read Re: RMP # 48
L. Cooper
10/10/07
Read Re: RMP # 48
Franz Gnaedinger
10/11/07
Read Re: RMP # 48
Franz Gnaedinger
10/11/07
Read Re: RMP # 48
L. Cooper
10/12/07
Read Re: RMP # 48
Franz Gnaedinger
10/12/07
Read Re: RMP # 48
Franz Gnaedinger
10/12/07
Read Re: RMP # 48
L. Cooper
10/13/07
Read Re: RMP # 48
Franz Gnaedinger
10/13/07
Read Re: RMP # 48
L. Cooper
10/13/07
Read Re: RMP # 48
Franz Gnaedinger
10/15/07
Read Re: RMP # 48
Franz Gnaedinger
10/18/07
Read Discussion of error/mistake in Greek texts
Ed Wall
10/19/07
Read Re: Discussion of error/mistake in Greek texts
Franz Gnaedinger
10/20/07
Read Re: Discussion of error/mistake in Greek texts
Milo Gardner
12/5/07
Read Re: Discussion of error/mistake in Greek texts
Milo Gardner
12/14/07
Read Re: Discussion of error/mistake in Greek texts
Franz Gnaedinger
12/14/07
Read Re: Discussion of error/mistake in Greek texts
Milo Gardner
12/14/07
Read Schools of Egyptology, and why they are not leaders in scribal math studies
Milo Gardner
10/11/07
Read Re: RMP # 48
Milo Gardner
10/12/07
Read Re: RMP # 48
L. Cooper
10/12/07
Read Re: RMP # 48
Milo Gardner
10/13/07
Read Re: RMP # 48
L. Cooper
7/11/10
Read Re: RMP # 48
Dioxippus
7/12/10
Read Re: RMP # 48
Milo Gardner
7/20/10
Read Re: RMP # 48
Dioxippus
7/21/10
Read Re: RMP # 48
Milo Gardner
7/21/10
Read Re: RMP # 48
Dioxippus
7/21/10
Read Re: RMP # 48
Milo Gardner
7/23/10
Read Re: RMP # 48
Dioxippus
7/23/10
Read Re: RMP # 48
Milo Gardner
10/6/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/8/07
Read Re: RMP # 48
Milo Gardner
10/11/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/12/07
Read Re: RMP # 48
Milo Gardner
10/13/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/13/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/19/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/27/07
Read Re: RMP # 48
Matt Hugh

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.