# Talk:Red auxiliary number

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Field: History of mathematics

## Discussion

David,

What are you thinking of when you ask for additional footnotes? Be specific! The "Crest of the Peacock" citation, offers direct chapter and verse related to three practice problems that Ahmes detailed to learn the method. Have you worked even one of the problems, i.e. RMP 23? Beyond Ahmes' practice problems you may rhetorically7 claim that red auxiliary numbers were not applied to create optimized, but not an optimal, 2/n table --- but if you do - you must be specific!

That is, Rhetoric is one thing. Mathematics and science are two deeper subjects. I have shown that every 51 2/n problem followed the three RM- 21, 22, and 23 practice problems. Ahmes easily practiced selecting LCM's to solve a series of unit fractions summed to a given number, as anyone can see by working the practice problems. Like arithmetic progressions, red auxiliary number selections Ahmes used a central formula, and altered its parameters working problems forwards, backwards, and in the middle.

Moreover, all 26 EMLR 1/p and 1/pq conversion problems also practiced selecting non-opimtal LCM's, a second level that confirms the scientific hypothesis that Ahmes had used the red auxiliary numbers to create his 2/n table and complete the conversion of any n/p or n/pq vulgar fraction to an 'optimized' - but not always optimal -- Egyptian fraction remainder.

The remainder topic is a subject is also critical to the red auciliary debate, another issue that you may be silently protesting, asking for a 'sky hook' to hang your algorithmic view of Ahmes' arithmetic. Ahmes used no central algorithms, despite several U.K. universities suggesting that you are on a productive path.

The best, and likely the only path, to decode Ahmes RMP is to work every one of his 84 problems and 51 2/n table entries, forwards,. backwards and in the middle, changing any parameter in each formula that entered the text.

Best Regards,

~Milogardner

As I just wrote on my talk: I'm thinking that the whole thing looks like original research and I would like citations to people other than you who use the exact phrase "red auxiliary number" as well as citations to papers in which each of the various statements you make in the article can be found. As for your edit summary, "David Eppstein does not respond to his personal Wiki talk pape": you left your comment at 5AM my time; it's unreasonable to expect an immediate response at that hour. —David Eppstein (talk) 15:05, 1 November 2008 (UTC)