
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 parallelepiped, '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 quadruplehekat
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

