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Re: Prime numbers and pi
Posted:
Apr 26, 2009 10:01 AM
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Franz,
You keep changing the subject to ones that have no solution that was known to Ahmes. Ahmes' addition, subtraction, multiplication and division methods had changed the arithmetic operations and notations used in the Old Kingdom.
You keep applying the binary Old Kingdom method, used only for Ahmes proofs --- and not initial calculations. Ahmes' arithmetic methods used in the Middle Kingdom - as the RMP clearly reports -- can only be seen after stripping Egyptian fraction notation, as summarized by:
http://ahmespapyrus.blogspot.com/2009/01/ahmes-papyrus-new-and-old.html
from the text.
Your work offers no clue on how to read Ahmes' 2/n table and conversions of rational numbers to optimized unit fraction series. You muddle through like an Englishman (ala Peet) -- by suggesting light -- where there is only darkness!
You speak of the conversion of 63/64, which was easily written as (32 + 16 + 8 + 4 + 2 + 1)/64, as Ahmes used when stating binary quotients, as the dominate notation of the Old Kingdom. In the Middle Kingdom, as Tanja Pemmerening reported in 2002, the 1/64 hekat unit was 'healed', as she fairly reported a dja as 1/64 of a hekat in the Ebers Papyrus, and finalized in her 2005/2006 PhD thesis.
As you know, the Old Kingdom Horus-Eye series only summed to 63/64, throwing away a 1/64 unit - or terrible round-off error.
The Akhmim Wooden Tablet, Kahun P. and all other Middle Kingdom texts solved the problem, in terms of hekat division, by writing
(64/64)/n = Q/64 + (5R/n)*1/320
with Q = quotient, R = remainder and 1/320 = ro, scaled by (5/5).
Of course, Ahmes also divided 10 hekat by writing as 3200 ro in the context:
3200/n = Q + R
as the RMP 66 divided 3200 by 365 with Q = 8 and R = 280/365, scaled to (6/6) (as Robin-Shute and other 20 century scholars like Peet, Chace, Gillings, et al, did not fairly report.
That is, please stop baiting Ahmes' text and switching to an unknown text that is unreadable, and suggesting that Ahmes' text was unreadable. Ahmes' text is readable in almost every respect. There are of course minor issues that are unreadable in the RMP, issues that we can discuss at another time.
Best Regards,
Milo
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