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Recreational Mathematics Magazine

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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


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 The first is by Luca Pacioli and was previously unpublished.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


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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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