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Re: Who discovered irrational numbers?
Posted:
Mar 24, 2009 11:24 AM
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Breaking the 2/nth table code, be it from the RMP, Kahun or the EMLR, requires the understanding of multipliers and aliquot parts.
Concerning the RMP 2/n table, it number theory building blocks were fully broken a few years ago, as noted by:
http://rmprectotable.blogspot.com/
The first 3-term series was 2/13. Its multiplier was 8, solved by considering the aliquot parts of 104 (104, 52, 26, 13, 8, 4, 2, 1) allowing:
2/13*(8/8) = 16/104 = (13 + 2 + 1)/104 = 8' 52' 104'
Ahmes used 15 different multipliers (2, 3, 4, 6, 8, 12, 20, 24, 30, 36, 40, 42, 56, 60, and 70) to convert 51 2/n rational numbers to optimized unit fraction series.
Scribes were free to choose their own set of highly composite multipliers, thereby showing off their skills in offering optimized, but not always optimal, unit fraction series.
Concerning 2/13, 10 could have been used. Ahmes used 20, 30, 49, 60 and 70, so why not 10?
The answer may be connected to Ahmes' use of three Horus-Eye numbers (2, 4, and 8) as multipliers. Note 2/13 used eight (8) as the only Horus-Eye multiplier used for a 2/p conversion. That is, Ahmes may have been making a point about inadequate aspects of binary numbers as multipliers. Of course, 2 and 4 were used several times for 2/pq, composite number, conversions.
Cutting a review of this topic short, Ahmes' understanding of multipliers and aliquot parts was considerable.
Best Regards,
Milo Gardner
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