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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

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