×

Who introduced Western mathematicians to Latin squares? (English) Zbl 1421.01009

The author considers two questions. The first is who proved the first concrete depiction of a Latin square in Western mathematics. The second is who was the first to prove an analytic description of a Latin square in Western mathematics. The author makes a case for why Ozanam is the answer to the first question (and not Bachet). He also makes a case for why Euler is the answer to the second question.

MSC:

01A45 History of mathematics in the 17th century
01A50 History of mathematics in the 18th century
05-03 History of combinatorics
05B15 Orthogonal arrays, Latin squares, Room squares
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andersen, Lars Døvling; Wilson, Robin; Watkins, John J., Latin squares, Combinatorics: Ancient and modern, 251-284 (2013), Oxford, UK: Oxford University Press, Oxford, UK · Zbl 1321.01007
[2] Bachet, Claude Gaspar, Problèmes plaisans et délectables, qui se font par les nombres (1612), Lyon, France: Rigaud, Lyon, France · Zbl 0089.00402
[3] Bachet, Claude Gaspar, Problèmes plaisans et délectables, qui se font par les nombres (1624), Lyon, France: Rigaud, Lyon, France · Zbl 0089.00402
[4] Bachet, Claude-Gaspar; Labosne, A., Problèmes plaisants et délectables, qui se font par les nombres (1874), Paris, France: Gauthier-Villiers, Paris, France
[5] Droesbeke, Jean-Jacques; Fine, Jeanne; Saporta, Gilbert; Droesbeke, Jean-Jacques; Fine, Jeanne; Saporta, Gilbert, Le cheminement historique des plans d’expériences, Plans d’expériences: Applications à l’entreprise, 1-12 (1997), Paris, France: Éditions Technip, Paris, France · Zbl 0947.62504
[6] Dudeney, Henry Ernest, Amusements in mathematics (1917), London, UK: Nelson, London, UK
[7] Emanouilidis, Emanuel, Latin and magic squares, International Journal of Mathematical Education in Science and Technology, 36, 5, 546-549 (2005)
[8] Euler, Leonhard, Recherches sur une nouvelle espèce de quarrés magiques, Verhandelingen uitgegeven door het zeeuwsch Genootschap der Wetenschappen te Vlissingen, 9, 4, 85-239 (1782)
[9] Keedwell, Anthony Donald; Dénes, József, Latin squares and their applications (2015), Amsterdam, The Netherlands: North-Holland, Amsterdam, The Netherlands · Zbl 1318.05001
[10] Kendall, Maurice George, Who discovered the Latin square?, The American Statistician, 2, 4, 13 (1948)
[11] Klyve, Dominic; Stemkoski, Lee, Graeco-Latin squares and a mistaken conjecture of Euler, College Mathematics Journal, 37, 1, 2-15 (2006) · doi:10.1080/07468342.2006.11922160
[12] Knuth, Donald Ervin, The art of computer programming, Vol. 4A: Combinatorial algorithms, Part 1 (2011), Upper Saddle River, NJ: Addison-Wesley, Upper Saddle River, NJ · Zbl 1170.68411
[13] Labosne, A., Problèmes de mathématiques et de physique: Problèmes de physique (1856), Paris, France: Librairie de Dezobry, E Magdeleine et Cie, Paris, France
[14] Labosne, A., Problèmes de mathématiques et de physique: Problèmes de mathématiques (1857), Paris, France: Librairie de Dezobry, E Magdeleine et Cie, Paris, France
[15] O’Connor, John J.; Robertson, Edmund Frederick, Jacques Ozanam (2002), St. Andrews, UK: University of St. Andrews, School of Mathematics and Statistics, St. Andrews, UK
[16] O’Connor, John J.; Robertson, Edmund Frederick, Claude Gaspar Bachet de Méziriac (2006), St. Andrews, UK: University of St. Andrews, School of Mathematics and Statistics, St. Andrews, UK
[17] Ozanam, Jacques, Récréations mathématiques et physiques (1694), Paris, France: Jombert, Paris, France
[18] Ozanam, Jacques, Récréations mathématiques et physiques (1723), Paris, France: Jombert, Paris, France
[19] Richardson, John Thomas Edwin, The use of Latin-square designs in educational and psychological research, Educational Research Review, 24, 1, 84-97 (2018)
[20] Roberts, Fred Stephen; Tesman, Barry, Applied combinatorics (2009), Boca Raton, FL: CRC Press, Boca Raton, FL · Zbl 1184.05001
[21] Singmaster, David, Sources in recreational mathematics: An annotated bibliography (2004)
[22] Ullrich, Peter, Officers, playing cards, and sheep: On the history of Eulerian squares and of the design of experiments, Metrika, 56, 3, 189-204 (2002) · Zbl 1433.62015
[23] Wallis, Walter D.; George, John C., Introduction to combinatorics. : (2011), Boca Raton, FL: CRC Press, Boca Raton, FL
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.