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Topic: RMP 66, its initial calculation and diplation proof
Replies: 62   Last Post: May 18, 2009 2:26 AM

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 Milo Gardner Posts: 1,105 Registered: 12/3/04
RMP 66, its initial calculation and diplation proof
Posted: Apr 29, 2009 9:11 AM

Dear Forum members:

Per Franz's request, RMP 66 is reported in a separtate thread. To revview RMP 66 in detail, step-by-step, let's start at the beginning, the initial calculation and follow Ahmes' outline.

Ahmes omitted steps, leaving serious logical gaps in all of his problems. Peet, Chace, Gillings and Robins-Shute avoided filling the logical gaps by changing the subject to misleading and, at times, incorrect topics. Using RMP 66 as an example, 20th century scholars had not fairly followed Ahmes' outline of the initial problem, as well as Ahmes' matched duplation proof, thereby, not revealing their scholarly oversights of Ahmes' actual Middle Kingdom arithmetic thinking (translated into modern arithmetic).

Ahmes proved the correctness of answers, sometimes completely, sometimes not, by the well-known binary multiplication method. In RMP 66, Ahmes showed the answer of dividing 10 hekat of fat, written as 3200 ro by 365, the number of days in the year, gaining a theoretical daily usage by showing:

3200/365 = 8 + 280/365

To obtain the answer Ahmes had literally scaled the remainder 280/365 by 6/6 such that:

1680/2190 = 8 +(1460 + 219 + 1)/2190

= 8 + 2/3 + 1/10 + 2190

as the RMP 2/n table was built.

Ahmes' proof broke up the quotient 8 into two parts: 5 ro, which equals 1/64 of a hekat, and 3 ro. Ahmes did not calculate the quotient 8 by applying the Old Kingdom multiplication proof. Ahmes did calculate the remainder's three unit fractions by the traditional duplation proof.

In summary, as a matched pair, Ahmes' initial calculation of (8 + 2/3 + 1/10 + 1/2190) ro, based in applying the 2/n table's method (selected the LCM 6), and the Old Kingdom duplation proof for the remainder's three-terms, were not discussed by Peet, Chace, Gillings, Robins-Shute, and other 20th century scholars.

Comments from Franz, and/or Math forum members would be appreciated on RMP 66. Please feel free to include your view(s) of the general implications of the RMP's initial calculations and duplation proofs reported fairly and/or unfairly by 20th and 21st century scholars.

Best Regards,

Milo Gardner