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Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project

Received: 11 April 2017     Accepted: 26 April 2017     Published: 21 June 2017
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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.

Published in History Research (Volume 5, Issue 3)
DOI 10.11648/j.history.20170503.11
Page(s) 16-21
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Rhind Papyrus, 2/n table, Egyptian Fractions

References
[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).
Cite This Article
  • APA Style

    Lionel Bréhamet. (2017). Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project. History Research, 5(3), 16-21. https://doi.org/10.11648/j.history.20170503.11

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    ACS Style

    Lionel Bréhamet. Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project. Hist. Res. 2017, 5(3), 16-21. doi: 10.11648/j.history.20170503.11

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    AMA Style

    Lionel Bréhamet. Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project. Hist Res. 2017;5(3):16-21. doi: 10.11648/j.history.20170503.11

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  • @article{10.11648/j.history.20170503.11,
      author = {Lionel Bréhamet},
      title = {Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project},
      journal = {History Research},
      volume = {5},
      number = {3},
      pages = {16-21},
      doi = {10.11648/j.history.20170503.11},
      url = {https://doi.org/10.11648/j.history.20170503.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.history.20170503.11},
      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.},
     year = {2017}
    }
    

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Author Information
  • Independent Scholar, Bordeaux, France

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