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Re: Prime numbers and pi
Posted:
Apr 25, 2009 3:35 AM


Milo, please read the Rhind Mathematical Papyrus as written. Your method is not the one used by Ahmes.
The Horus eye series '2 '4 '8 '16 '32 '64 plays a role in astronomy. A month of 30 days multiplied by '2 '4 '8 '16 '32 '64 yields a lunation of 29 '2 '32 days, or 29 days 12 hours 45 minutes, average modern value 19d 12h 45m 2.9s, mistake of the ancient value less than one minute per lunation, or half a day in a lifetime. The Egyptians knew of course that the mathematical series is infinite:
1 = '1 1 = '2 '2 1 = '2 '4 '4 1 = '2 '4 '8 '8 1 = '2 '4 '8 '16 '16 1 = '2 '4 '8 '16 '32 '32 1 = '2 '4 '8 '16 '32 '64 '64
1 = '2 '4 '8 '16 '32 '64 '128 '256 '512 '1024 ...
The confusion about the Horus eye series concerns the term "the whole one"  not one as number, but one lunation, a whole lunation.
Starting from 1 = '1 and 1 = '2 '2 you can get another stairway and infinite series. The new resolution of 1 is '2 '3 '6 that frequently occurs in the RMP. Then we need the resolution 1 = '2 '4 '6 '12 that is also present in the RMP. It occurs in the division of 2 by 95 with the help of the auxiliary number 60. Ahmes carries out the following calculations, as you can see when you read the RMP in the original, instead of just consulting the 2/n table:
2 divided by 95 equals '60 plus ???
95 divided by 60 equals 1 '2 '12
2 minus 1 '2 '12 equals '4 '6
result '60 plus '4x95 '6x95
2 divided by 95 equals '60 '380 '570
The pleasing part is how a division of 2 turns into a subtraction from 2. This method requires the knowledge of many resolutions of 2. The one applied here is
2 = 1 '2 '4 '6 '12
and the basic resolution of 1 is
1 = '2 '4 '6 '12
Now we have
1 = '1 1 = '2 '2 1 = '2 '3 '6 1 = '2 '4 '6 '12
Rearranging the terms
1 = '1 1 = '2 '2 1 = '2 '6 '3 1 = '2 '6 '12 '4
and factorizing them
1 = '1 1 = '1x2 '2 1 = '1x2 '2x3 '3 1 = '1x2 '2x3 '3x4 '4
Prolong the stairway in this form and you obtain another infinite series:
1 = '1x2 '2x3 '3x4 '4x5 '5x6 '6x7 '7x8 '8x9 ...
Regards, Franz Gnaedinger



