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Topic: Prime numbers and pi
Replies: 33   Last Post: Dec 10, 2012 3:43 PM

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Franz Gnaedinger

Posts: 330
Registered: 4/30/07
Re: Prime numbers and pi
Posted: Apr 28, 2009 2:56 AM
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Milo, consulting the 2/n table is not enough, you have
to study the actual "working out" performed by Ahmes.

Here a postscript regarding RMP 66. Ahmes divides
a yearly supply of 10 hekat of fat by 365 and obtains
8 "3 '10 '2190 ro as daily portion. He then gives the
result in a second form, as '64 hekat 3 "3 '10 '2190 ro.
Why this conversion?

RMP 38 led me to the following containers, inner
measurements:

Right parallel-epiped, '2 by '3 by '5 royal cubits,
or 210 by 140 by 84 Qebhsenuf marks, diagonal exactly
266 Qebhsenuf marks, capacity exactly one hekat

Cylinder, diameter 7 fingers or one fourth of a cubit,
circumference 22 fingers, height 19 fingers, capacity
0.999728... or practically one hekat

Cylinder, diameter 14 fingers or half a cubit,
circumference 44 fingers, height 19 fingers, capacity
3.997115... hekat or practically one quadruple-hekat

Now RMP 66 may suggest a couple more containers,
inner measurements again:

Cube, 9 by 9 by 9 fingers, capacity 0.99626... or
practically one hekat

Cube, 4 '2 by 4 '2 by 4 '2 fingers, or 9 by 9 by 9
Ra marks, capacity 0.124533... or practically '8 of
a hekat

Cube, 2 '4 by 2 '4 by 2 '4 fingers, or 9 by 9 by 9
Shu marks, capacity 0.015566... or practically '64
of a hekat

By combining 9 fingers and 9 Ra marks and 9 Shu marks
you can get a set of rectangular containers of 1 and
'2 and '4 and '8 and '16 and '32 and '64 hekat (or
320 and 160 and 80 and 40 and 20 and 10 and 5 ro)

Cylinder, diameter 1 finger, height 3 fingers,
capacity 1.030405... or practically one ro

The daily portion of fat is then one small cube
('64 hekat or 5 ro) and three full (3 ro) and one
almost full ("3 '10 '2190) small cylinders.

The tomb of Hesy, Third Dynasty, shows interesting
drawings: tools, games, rulers, a double set of
weights, and a double set of cylindrical containers,
fourteen each, steadily increasing, from small
containers to barrels, proving that already the
Old Kingdom used an elaborate metrological system.

Regards, Franz Gnaedinger


Date Subject Author
4/12/09
Read Prime numbers and pi
James A. Landau
4/13/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/13/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/13/09
Read Re: Prime numbers and pi
James A. Landau
4/14/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/14/09
Read Re: Prime numbers and pi
Franz Gnaedinger
6/26/12
Read Re: Prime numbers and pi
hashim shah
4/14/09
Read Re: Prime numbers and pi
James A. Landau
4/15/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/18/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/18/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/23/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/23/09
Read Re: Prime numbers and pi
Milo Gardner
4/25/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/25/09
Read Re: Prime numbers and pi
Milo Gardner
4/26/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/26/09
Read Re: Prime numbers and pi
Milo Gardner
4/27/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/27/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/27/09
Read Re: Prime numbers and pi
Milo Gardner
4/28/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/28/09
Read Re: Prime numbers and pi
Milo Gardner
4/29/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/15/09
Read Re: Prime numbers and pi
John Bibby, QED of York, York, England
6/27/12
Read Re: Prime numbers and pi
Milo Gardner
6/27/12
Read Re: Prime numbers and pi
Milo Gardner
12/5/12
Read Re: Prime numbers and pi
kevin
12/6/12
Read Re: Prime numbers and pi
Milo Gardner
12/10/12
Read Re: Prime numbers and pi
Milo Gardner

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