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Recreational Mathematics Magazine

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Mathematical Citation Quotient (MCQ) 2016: 0.05

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2182-1976
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"A difficult case": Pacioli and Cardano on the Chinese Rings

Albrecht Heffer
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  • Center for History of Science, Ghent University, Mathematics Department, LMU Munich, Munich, Germany
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/ Andreas M. Hinz
Published Online: 2018-01-11 | DOI: https://doi.org/10.1515/rmm-2017-0017

Abstract

The Chinese rings puzzle is one of those recreational mathematical problems known for several centuries in the West as well as in Asia. Its origin is diffcult to ascertain but is most likely not Chinese. In this paper we provide an English translation, based on a mathematical analysis of the puzzle, of two sixteenth-century witness accounts. The first is by Luca Pacioli and was previously unpublished. The second is by Girolamo Cardano for which we provide an interpretation considerably different from existing translations. Finally, both treatments of the puzzle are compared, pointing out the presence of an implicit idea of non-numerical recursive algorithms.

Keywords: Chinese rings; recreational problems; Pacioli; Cardano

References

  • [1] Ahrens, Wilhelm. Mathematische Unterhaltungen und Spiele, Leipzig: B.G., Teubner, 1901.Google Scholar

  • [2] Arima, Yoriyuki. Shüki sanpō, [Edo]: Senshōdō, 1769.Google Scholar

  • [3] Ball, W. W. Rouse. Mathematical recreations and problems of past and present times, London: Macmillan and Co, 1892.Google Scholar

  • [4] Boncompagni, Baldessaro. \Appendice di documenti inediti relativi a Fra Luca Pacioli", Bullettino di bibliografia e di storia delle scienze matematiche e fisiche, 12 (June), 428-438, 1879.Google Scholar

  • [5] Cardano, Girolamo. Practica arithmetice & mensurandi singularis: in qua que preter alias continentur versa pagina demonstrabit, Mediolani: Io. Antonins Castellioneus Mediolani imprimebat, impensis B. Calusci, 1539.Google Scholar

  • [6] Cardano, Girolamo. Hieronymi Cardani Medici Mediolanensis De Subtilitate Libri XXI, Norimbergæ apud Ioh. Petreium (for a modern edition and translation, Forrester), 1550.Google Scholar

  • [7] Döll, Steffen; Hinz, Andreas M. \Kyü-renkan|the Arima sequence", Advanced Studies in Pure Mathematics, to appear.Google Scholar

  • [8] Dudeney, Henry Ernest. Amusements in Mathematics, London: Thomas Nelson, 1917.Google Scholar

  • [9] Fibonacci, Leonardo. Scritti di Leonardo Pisano, Baldassarre Boncompagni (ed.), Roma: Tipografia delle scienze matematiche e fisiche, 1857 (English translation by Laurence Sigler, Fibonacci's Liber Abaci: a Translation into Modern English of Leonardo Pisano's Book of Calculation, New York: Springer, 2002).Google Scholar

  • [10] Forrester, John (ed. tr.). The De subtilitate of Girolamo Cardano, Tempe, Arizona: Arizona Center for Medieval and Renaissance Studies, 2013.Google Scholar

  • [11] Garlaschi Peirani, Maria (ed.). De viribus quantitatis, Milano: Ente Raccolta Vinciana, 1997.Google Scholar

  • [12] Gardner, Martin. Knotted doughnuts and other mathematical entertainments, New York: W.H. Freeman, 1986.Google Scholar

  • [13] Gros, Louis. Théorie du Baguenodier par un clerc de notaire lyonnais, Lyon: Aimé Vingtrinier, 1872.Google Scholar

  • [14] Heeffer, Albrecht. \Regiomontanus and Chinese Mathematics", Philosophica, 83, 81-107, 2010.Google Scholar

About the article

Published Online: 2018-01-11

Published in Print: 2017-12-20


Citation Information: Recreational Mathematics Magazine, Volume 4, Issue 8, Pages 5–23, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2017-0017.

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© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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