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