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Re: Egyptian fraction math only used quotient and remainder statements
Posted:
Dec 16, 2011 2:55 PM
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Updating this view: Many 20th century scholars diverted attention from scribal rational number conversion methods due to their lack of understanding of the scribal conversion of 5/19 in RMP 32 that reported
1 + 1/6 + 1/12 + 1/114 + 1/228
1. Ahmes may have converted 5/19 by an EMLR method
5/19 x (6/6) = 30/114 = (19 + 1)/114 + 10/114
5/57 x (12/12) = 60/684 = (57 + 3)/684 = 1/12 + 1/228
and recorded
1 + 1/6 + 1/12 + 1/114 + 1/228
This view was taken from the EMLR conversion of 1/8 and 1/16 by 25/25 and 6/6.
2. Ahmes likely only used 12/12 that converted 5/19 by:
1 + (5/19)x (12/12) = 1 + 60/228 = 1 + (38 + 19 + 2 + 1)/228 =
1 + 1/6 + 1/12 + 1/114 + 1/228
3. I'll be re-reading Ahmes' shorthand to validate the red auxiliary numbers that were recorded.
If (38 + 19 + 2 + 1) were cited, the second method would be confirmed.
Best Regards to all,
Milo Gardner
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