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Milo Gardner

Posts: 1,105
Registered: 12/3/04

RMP 47, 82 and 83
Posted: Apr 1, 2009 7:13 PM

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RMP 47, 82 and 83 were division of hekat problems. The 36 RMP examples and 6 Akhmim Wooden Tablet examples were solved in 2005 (http://www.mathorigins.com/image%20grid/awta.htm).

RMP 47 cites a complex example, dividing 100 hekat, written as (6400/64), by 70. The quotient 91/64 and remainder 30/64 were written in binary (Horus-Eye)(64 + 16 + 8 + 2 + 1)/64 units and scaled 1/320, (150/70)ro unit, quotient 2 and remainder 1/7, respectively, reporting.

Robins-Shute understood aspects of RMP 47 by finding the correct final answer, garbling the beginning and intermediate steps in 1987, but missed the point that divisors n could increase as the hekat numerator increased.

RMP 82 listed 29 examples of dividing one hekat, written as 64/64, divided by 29 rational numbers n, in the range 1/64 < n < 64. The 29 problems reported binary quotients and ro scaled remainders that followed the RMP 47 example, related facts missed by 20th century scholars.

The table of 29 quotient and remainder answers were additional converted into unscaled equivalent hin, 1/10 of a hekat unit, showing that Ahmes generally found hin units by writing 10/n hin statements.

Tanja Pemmerening pointed out corrected aspects of the unscaled 64/n dja and 320/n ro statements in 2002 and 2005.

RMP 83, the bird-Feeding rate problem, was not correctly read by Chace, nor by other 20th century scholars. Today the 1900 BCE Akhmim Wooden Tablet, and its six division problems, allows a clear view of the division of one hekat, written as 64/64, divided by n. In RMP 83 n= 6, 20 and 40. Division took place by multiplying 1/6, 1/20 and 1/40. Ahmes' answer calculated 5/8 of a hekat, the amount of grain eaten by six birds in one day.

As usual, Ahmes began the hekat division discussion by beginning with the more complex example(s), and proceeding to the simpler examples.

Comments would be appreciated.

Milo Gardner