The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus

Carlos Dorce

doi:doi:10.11648/j.history.20180602.11

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The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus

Carlos Dorce

Published in History Research (Volume 6, Issue 2)

Received: 1 December 2018 Accepted: 21 December 2018 Published: 14 February 2019

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Abstract

The Rhind Mathematical Papyrus contains in the fragment known as the Recto Table the division of 2 by all the odd integer numbers from 3 to 101. This table hides the secret of how it was computed by its ancient Egyptian author because, till now, there is not a set of established known assumptions which allow compute all its values without any exception. In this paper, the algorithm which computes all the Recto Table is going to be established except three cases (denominators n = 35, 91 ad 95) which are calculated using another formula and the final denominator n = 101 which is a rareness.

Published in	History Research (Volume 6, Issue 2)
DOI	10.11648/j.history.20180602.11
Page(s)	33-49
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), 2019. Published by Science Publishing Group

Keywords

History of Mathematics, Rhind Papyrus, Kahun Papyrus, Recto Table, Prime Numbers, Algorithm, Unit Fractions

References

[1]	Abdulaziz, A. A. (2008). On the Egyptian method of decomposing 2/n into unit fractions. Historia Mathematica 35, 1-18.
[2]	Boyer, C. B. (1989). A History of Mathematics, second ed. Wiley, New York.
[3]	Bréhamet, L. (2014). Remarks on the Egyptian 2/D table in favor of a global approach (D prime number). 16 pages. 2014.
[4]	Bréhamet, L. (2014). Remarks on the Egyptian 2/D table in favor of a global approach (D composite number). 9 pages. 2014.
[5]	Bréhamet, L. (2017). Egyptian 2/D Table (D Prime Number): An Entirely New Analysis Consistent with the Idea of a Progressive Teamwork. History Research 5 (2), 17-29.
[6]	Bruins, E. M. (1952). Ancient Egyptian Arithmetic. Kon. Nederland Akademie van Wetenschappen, Ser. A, Vol. 55, No. 2, 81-91.
[7]	Bruins, E. M. (1975). The part in ancient Egyptian mathematics. Centaurus 19, 241-251.
[8]	Bruckheimer, M. & Salomon, Y. (1977). Some comments on R. J. Gillings's analysis of the 2/n table in the Rhind Papyrus. Historia Mathematica 4, 445-452.
[9]	Chace, A. B. (1927). The Rhind mathematical papyrus, Bristish Miseum 10057 and 10058. Volume I: free translation and commentary. Oberlin, Ohio: Mathematical Association of America.
[10]	Dorce, C. (2013). Història de la matemàtica. Des de Mesopotàmia fins al Renaixement. Barcelona: Publicacions i Edicions de la Universitat de Barcelona.
[11]	Dorsett, C. (2008). A Solution for the Rhind Papyrus unit fraction decompositions. Texas College Mathematics Journal 5, Number 1, 1-4.
[12]	Eisenlohr, A. (1877). Ein mathematisches Handbuch der alten Agypter (Papyrus Rhind des British Museum). Lepizig: J. C. Hinrich.
[13]	Gardner, M. (2008). Mathematics in Egypt: Mathematical Leather Roll. In Selin, H. (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer. Vol 1, 1385-1387.
[14]	Gardner, M. (2008). RMP 2/n table. http://rmprectotable.blogspot.com.
[15]	Gillings, R. J. (1972). Mathematics in Time of the Pharaohs. MIT Press, Cambridge, MA.
[16]	Gong, K. (1992). Egyptian Fractions. Math 196 Sprong 1992. UC Berkeley.
[17]	Griffith, F. L. L. (ed.) (1897). The Petrie Papyri: hieratic papyri from Kahun and Gurob (principally of the Middle Kingdom), Band 1: Text. London: Bernard Quaritch.
[18]	Knorr, W. (1982). Techniques of fractions in ancient Egypt and Greece. Historia Mathematica 9, 133-171.
[19]	Loria, G. (1892). Congetture e ricerche sull' aritmetica degli antichi Egiziani. Biblioteca Mathematica, series 2, Vol. 6, 97-109.
[20]	Peet, T. E. (1923). The Rhind Mathematical Papyrus, British Museum 10057 and 10058. London: The University Press of Liverpool limited and Hodder-Stoughton limited.
[21]	Sylvester, J. (1880). On a point in the Theory of Vulgar Fractions. American Journal of Mathematics 3(4), 332-335.
[22]	Van der Waerden, B. L. (1980). The (2:n) table in the Rhind Papyrus. Centaurus 23, 259-274.

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Carlos Dorce. (2019). The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus. History Research, 6(2), 33-49. https://doi.org/10.11648/j.history.20180602.11

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Carlos Dorce. The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus. Hist. Res. 2019, 6(2), 33-49. doi: 10.11648/j.history.20180602.11

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Carlos Dorce. The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus. Hist Res. 2019;6(2):33-49. doi: 10.11648/j.history.20180602.11

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@article{10.11648/j.history.20180602.11,
  author = {Carlos Dorce},
  title = {The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus},
  journal = {History Research},
  volume = {6},
  number = {2},
  pages = {33-49},
  doi = {10.11648/j.history.20180602.11},
  url = {https://doi.org/10.11648/j.history.20180602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.history.20180602.11},
  abstract = {The Rhind Mathematical Papyrus contains in the fragment known as the Recto Table the division of 2 by all the odd integer numbers from 3 to 101. This table hides the secret of how it was computed by its ancient Egyptian author because, till now, there is not a set of established known assumptions which allow compute all its values without any exception. In this paper, the algorithm which computes all the Recto Table is going to be established except three cases (denominators n = 35, 91 ad 95) which are calculated using another formula and the final denominator n = 101 which is a rareness.},
 year = {2019}
}

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AB  - The Rhind Mathematical Papyrus contains in the fragment known as the Recto Table the division of 2 by all the odd integer numbers from 3 to 101. This table hides the secret of how it was computed by its ancient Egyptian author because, till now, there is not a set of established known assumptions which allow compute all its values without any exception. In this paper, the algorithm which computes all the Recto Table is going to be established except three cases (denominators n = 35, 91 ad 95) which are calculated using another formula and the final denominator n = 101 which is a rareness.
VL  - 6
IS  - 2
ER  -

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Author Information

Carlos Dorce

Faculty of Mathematics, University of Barcelona, Barcelona, Spain

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Carlos Dorce. (2019). The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus. History Research, 6(2), 33-49. https://doi.org/10.11648/j.history.20180602.11

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ACS Style

Carlos Dorce. The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus. Hist. Res. 2019, 6(2), 33-49. doi: 10.11648/j.history.20180602.11

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AMA Style

Carlos Dorce. The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus. Hist Res. 2019;6(2):33-49. doi: 10.11648/j.history.20180602.11

Copy | Download

@article{10.11648/j.history.20180602.11,
  author = {Carlos Dorce},
  title = {The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus},
  journal = {History Research},
  volume = {6},
  number = {2},
  pages = {33-49},
  doi = {10.11648/j.history.20180602.11},
  url = {https://doi.org/10.11648/j.history.20180602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.history.20180602.11},
  abstract = {The Rhind Mathematical Papyrus contains in the fragment known as the Recto Table the division of 2 by all the odd integer numbers from 3 to 101. This table hides the secret of how it was computed by its ancient Egyptian author because, till now, there is not a set of established known assumptions which allow compute all its values without any exception. In this paper, the algorithm which computes all the Recto Table is going to be established except three cases (denominators n = 35, 91 ad 95) which are calculated using another formula and the final denominator n = 101 which is a rareness.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus
AU  - Carlos Dorce
Y1  - 2019/02/14
PY  - 2019
N1  - https://doi.org/10.11648/j.history.20180602.11
DO  - 10.11648/j.history.20180602.11
T2  - History Research
JF  - History Research
JO  - History Research
SP  - 33
EP  - 49
PB  - Science Publishing Group
SN  - 2376-6719
UR  - https://doi.org/10.11648/j.history.20180602.11
AB  - The Rhind Mathematical Papyrus contains in the fragment known as the Recto Table the division of 2 by all the odd integer numbers from 3 to 101. This table hides the secret of how it was computed by its ancient Egyptian author because, till now, there is not a set of established known assumptions which allow compute all its values without any exception. In this paper, the algorithm which computes all the Recto Table is going to be established except three cases (denominators n = 35, 91 ad 95) which are calculated using another formula and the final denominator n = 101 which is a rareness.
VL  - 6
IS  - 2
ER  -

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