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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 27, 2009 5:26 AM

Milo, in your first message to this forum you called
yourself an amateur math-historian. Amateurs are known
for consulting only secondary literature, whereas
professionals go back to the primary sources. If you
wish to reach the status of a professional you have to
read the Rhind Mathematical Papyrus as written, and if
you don't like Peet you have to study the facsimile
table is not enough, you have to consider the actual
working out as performed by Ahmes:

Divide 2 by an odd number with the help of an auxiliary
number. How do you proceed? Divide the odd number by the
auxiliary number and subtract the resulting unit fraction
series from 2. An example:

2 divided by 83 equals '60 plus ???

83 divided by 60 equals 1 '3 '20

2 minus 1 '3 '20 equals '4 '5 '6

result '60 plus '4x83 '5x83 '6x83

2 divided by 83 equals '60 '332 '415 '498

The method used by Ahmes has an algebraic equivalent in

2/q = 1/p + (2 - q/p)/q

while your method, Milo, is based on the identity

2/q = 1/p + (2p - q)/pq

The Egyptians used algorithms, no algebra, so you have
to develop your method into a step by step procedure,
and then you have to bridge the gap between your method
and the one used by Ahmes (should not be so difficult).

In RMP 66 Ahmes divides a yearly portion of 10 hekat or
3200 ro of fat by 365 days and obtains 8 "3 '10 '2190 ro
as daily portion. Interestingly, in the contracts of
Hapzefa the daily portion is obtained from the yearly
by dividing not by 365 but by 360 days, testifying to
an ideal early year of 360 days as reconstructed in
the hypothetical very early myth going back to the era
of the Göbekli Tepe (Sanli-Urfa region, southeast
Anatolia, stone pillar temples 11 600 - 9 500 BP,
earth mound on top of the limestone hill even earlier).

Who says the Old Kingdom mathematicians knew only the
fractions '2 and '4 and '8 and '16 and '32 and '64 ?
They built pyramids but had no concept of one third
and one fifth and one sixth and one seventh and one
nineth and one tenth et cetera ??? I don't buy that.

Regards, Franz Gnaedinger