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Re: Rhind papyrus problem about harmonic mean
Posted:
Oct 18, 2012 7:34 PM
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Gillings, Mathematics in the Time of the Pharaohs. page 131 offers a harmonic mean discussion of RMP 76, with a few sentences:
"Now the pesu of the original 1,000 loaves was 10, so that the total number of loaves to be received in exchange is greater in the ratio of 24 is to 10, namely,
1,000 x 24/10 = 2,400 loaves
Then there will be a half of 2,400 or 1,200 loaves of each kind, pesu 20 and pesu 30, received in exchange for 1,000 loaves of pesu 10.
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It is interesting to note that how well Ahmose choose his two numbers 20 and 30 for the pseus.
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This is like Ahmose problem 76, for the answer to both problems is the harmonic means of 20 and 30, which is 24, and not 25 (the arithmetic mean). ..."
Clagett and others may report this problem differently. Robins and Shute did not mention RMP 76 at all in 1987.
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