Volume 5, Issue 3, May 2017, Page: 16-21
Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project
Lionel Bréhamet, Independent Scholar, Bordeaux, France
Received: Apr. 11, 2017;       Accepted: Apr. 26, 2017;       Published: Jun. 21, 2017
DOI: 10.11648/j.history.20170503.11      View  2515      Downloads  70
Abstract
This final approach implies that all alternative solutions were pre-calculated by the scribes. The classification parameter is the difference (s-r) between two divisors of D in the decompositions 2/D =1/D1+1/D2. Adequate adjustments of (s-r) provide a low limit (57) to the count of alternatives. A four-component generator (2/3, 2/5, 2/7, 2/11) operates as a (hidden) mother-table. Adding few logical rules of common sense is enough to find the reasons of the Egyptian choices. Even 2/95, not decomposable into two fractions but only into three, turns out quite explainable.
Keywords
Rhind Papyrus, 2/n table, Egyptian Fractions
To cite this article
Lionel Bréhamet, Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project, History Research. Vol. 5, No. 3, 2017, pp. 16-21. doi: 10.11648/j.history.20170503.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
L. BREHAMET: 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, pp. 17-29 (2017). See also L. BREHAMET: Remarks on the Egyptian 2/D table in favor of a global approach (D prime number), arXiv: 1403.5739 [math. HO] (2014).
[2]
M. CLAGETT: Ancient Egyptian Science: A source book, American Philosophical Society, Vol. 3, p. 113 (1999).
[3]
B. L. van der Waerden: “The (2:n) Table in the Rhind Papyrus”. Centaurus Vol. 23, 259–74 (1980). For a probable derivation of composites from prime numbers, see pp. 265– 66.
[4]
L. MIATELLO: “The Values in the Opening Section of the Rhind Mathematical Papyrus", Physis - Rivista Internazionale di Storia della Scienza Vol. 44, pp.327-347 (2007).
[5]
K. BROWN: The Rhind Papyrus 2/n Table (1995), available on the site http://www.mathspages.com/home/kmath340/kmath340.htm.
[6]
M. GARDNER: Egyptian fractions: Unit Fractions, Hekats and Wages - an Update (2013), available on the site of academia.edu. [Herein can be found an historic of various researches about the subject].
[7]
A. ABDULAZIZ: On the Egyptian method of decomposing 2/n into unit fractions, Historia Mathematica, Vol. 35, pp.1-18 (2008).
[8]
R. J. GILLINGS: Mathematics in the Time of Pharaohs, MIT Press (1972), reprinted by Dover Publications (1982).
[9]
E. M. BRUINS: The part in ancient Egyptian mathematics, Centaurus, Vol. 19, pp.241-251 (1975).
[10]
O. NEUGEBAUER: The Exact Sciences in Antiquity, Copenhague, Munksgaard, (ISBN 978-0486223322), 1951.
[11]
T. E. PEET: The Rhind Mathematical Papyrus, British Museum 10057 and 10058, London: The University Press of Liverpool limited and Hodder - Stoughton limited (1923).
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