Egyptian 2/D Table (D Prime Number): An Entirely New Analysis Consistent with the Idea of a Progressive Teamwork
History Research
Volume 5, Issue 2, March 2017, Pages: 17-29
Received: Oct. 8, 2016; Accepted: Feb. 17, 2017; Published: Apr. 1, 2017
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Lionel Bréhamet, Independent Scholar, Bordeaux, France
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For h=3 or 4, Egyptian decompositions into h unit fractions, like 2/D = 1 /D1 +... +1 /Dh, were given by using (h-1) divisors (di) of D1. This ancient modus operandi, well recognized today, provides Di=DD1/di for i greater than 1. Decompositions selected (depending on di) have generally been studied by modern researchers through the intrinsic features of di itself. An unconventional method is presented here without considering the di properties but just the differences dh-1- dh. In contrast to widespread ideas about the last denominator like ‘Dh smaller than 1000’, it is more appropriate to adopt a global boundary of the form ‘Dh smaller or equal to 10D’, where 10 comes from the Egyptian decimal system. Singular case 2/53 (with 15 instead of 10) is explained. The number of preliminary alternatives before the final decisions is found to be so low (71) for h=3 or 4 that a detailed overview was possible in the past. A simple additive method of trials, independent of any context, can be carried out, namely 2n+1= d2 +... + dh. Clearly the decisions fit with a minimal value of the differences dh-1- dh, independently of any di values.
Rhind Papyrus, 2/n Table, Egyptian Fractions
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Lionel Bréhamet, Egyptian 2/D Table (D Prime Number): An Entirely New Analysis Consistent with the Idea of a Progressive Teamwork, History Research. Vol. 5, No. 2, 2017, pp. 17-29. doi: 10.11648/j.history.20170502.11
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