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Re: Prime numbers and pi
Posted:
Apr 27, 2009 9:54 AM
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Franz,
Again, I agree with one of your main points, to read the RMP as Ahmes wrote it. To do that, Ahmes provided a decoding key, his 2/n table, a text that you have not read as written.
Once understanding Ahmes' method for converting rational numbers to optimized unit fraction series, as Ahmes himself studied the EMLR to learn the practice non-optimal methods, such as converting 1/8 to three scaling factors, namely:
1. 1/8 (3/3) = 3/24 = (2 + 1)/24 = 1/12 + 1/24
2. 1/8 (5/5) = 5/40 = (4 + 1)/40 = 1/10 + 1/40
3. 1/8 (25/25) = 25/200 and so forth using 6/6 as a remainder scaling numbers (cited in full yesterday) facts that Peet, Chace, et al, did not understand in 1927 when the EMLR was unrolled, or years thereafter.
Where is Peet's analysis of the EMLR? There are none that provide attested 1900 BCE arithmetic understandings of Ahmes 1650BCE method for converting 51 2/n rational numbers to optimized unit fraction series.
Given attested understandings of Ahmes 2/n table, and closely related methods for scaling hekat division problems, leared from another 1900 BCE source, the Akhmim Wooden Tablet, as explicitly cited on the math forum since 2005 --- four years in which experts and non-experts that privately disagree with the method, have not formally or informally disproven one aspect of RMP 81, 82 and other RMP problems that used the method.
Let the RMP speak for itself! That is, let Peet and Chace's transliterations of hieratic writing, often improperly written into hieroglyphic scrip, that avoided the required goal of translating the RMP into modern base 10 rational number arithmetic disappear, and become a footnote of history.
This July's conference in Mainz, Germany is finally putting together interdisciplinary teams to resolve the issues that you raise!
In summary, understanding Ahmes attested rational number conversion methods, methods that can and should be stripped away. When stripped of the Egyptian fraction notaiton, Ahmes' initial, intermediate and final calculations are exposed. Peet, Chace, Gillings, Robins-Shute and many other self pro-claimed experts never got that far. The 1920's scholar worked within muddled unit fraction binary thinking of their own making -- thereby not approaching Ahmes' abstract mathematical thinking, be the subject the arithmetic proportions used in RMP 40, 64 and the Kahun Papyrus -- that used a straight forward formula -- that Gauss learned by matching:
x1 + xn = x2 + x(n -1) = ... = x(n/2) = S/n
for odd-term series, such that the differential d, the number of terms in a seres n, the sum of the series S:
(d/2)(n-1) + S/n = xn
or another.
Q.E.D.
Milo Gardner
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