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

Lionel Bréhamet

doi:doi:10.11648/j.history.20170503.11

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

Lionel Bréhamet

Published in History Research (Volume 5, Issue 3)

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).

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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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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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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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TY  - JOUR
T1  - Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project
AU  - Lionel Bréhamet
Y1  - 2017/06/21
PY  - 2017
N1  - https://doi.org/10.11648/j.history.20170503.11
DO  - 10.11648/j.history.20170503.11
T2  - History Research
JF  - History Research
JO  - History Research
SP  - 16
EP  - 21
PB  - Science Publishing Group
SN  - 2376-6719
UR  - https://doi.org/10.11648/j.history.20170503.11
AB  - 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.
VL  - 5
IS  - 3
ER  -

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Author Information

Lionel Bréhamet

Independent Scholar, Bordeaux, France

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Plain Text BibTeX RIS

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}
}

Copy | Download

TY  - JOUR
T1  - Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project
AU  - Lionel Bréhamet
Y1  - 2017/06/21
PY  - 2017
N1  - https://doi.org/10.11648/j.history.20170503.11
DO  - 10.11648/j.history.20170503.11
T2  - History Research
JF  - History Research
JO  - History Research
SP  - 16
EP  - 21
PB  - Science Publishing Group
SN  - 2376-6719
UR  - https://doi.org/10.11648/j.history.20170503.11
AB  - 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.
VL  - 5
IS  - 3
ER  -

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