Fun sharpens the mind: How simple problems bring us closer to complex mathematical theories

Authors

  • Fernando Blasco Polytechnic University of Madrid (Spain).

DOI:

https://doi.org/10.7203/metode.15.27423

Keywords:

mathematics, recreational science, puzzles, problems, ingenuity

Abstract

This article presents a historical approach to recreational mathematics and the kinds of questions it deals with. I will present some authors, their works, the problems they contributed, and the fields of knowledge to which they gave rise, from Egyptian mathematics through the Renaissance and the Scientific Revolution to the 19th century, devoting a special section to the work of Leonhard Euler. I will present the problems, but not the solutions, so that the readers can actively participate by solving them or, if they wish, by checking the solutions in the references given.

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Author Biography

Fernando Blasco, Polytechnic University of Madrid (Spain).

Professor of Applied Mathematics at the Polytechnic University of Madrid (Spain). Since January 2018, he is a member of the Public Awareness Committee of the European Mathematical Society and since January 2020 he is the President of the Public Awareness Committee of the Spanish Royal Mathematical Society. Amateur magician and member of the Spanish Society of Illusionism. He has written five popular mathematics books and coordinated the publication of two others. Since 2013 he has collaborated with Radio Nacional de España (RNE), producing the «Matemáticas para todos» section of A hombros de gigantes .

References

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Bachet, C. G. (1624). Problèmes plaisants et délectables, qui se font par les nombres. P. Rigaud. https://gallica.bnf.fr/ark:/12148/bpt6k5818046p?rk=21459;2

Bossi, V. (2008). Magic and card tricks in Luca Paciolo’s De viribus quantitatis. In E. D. Demaine, M. L. Demaine, & T. Rodgers (Eds.), A lifetime of puzzles: A collection of puzzles in honor of Martin Gardner’s 90th birthday (pp. 123–129). A. K. Peters.

Dudeney, H. E. (1908). The Canterbury puzles, and other curious problems. E. P. Dutton and co. https://archive.org/details/117770747

Euler, L. (2007). Investigations on a new type of magic square (Traducción de A. Ho & D. Klyve). (Original work published in 1782). https://scholarlycommons.pacific.edu/euler-works/530/

Gardner, M. (1980). Carnaval matemático. Alianza Editorial.

Gardner, M. (1998). A quarter-century of recreational mathematics. Scientific American, 279(2), 68–75.

Gardner, M. (2001). The colossal book of mathematics: Classic puzzles, paradoxes, and problems. W. W. Norton & Company Inc.

Hirth, T. W. (2015). Luca Pacioli and his 1500 book De viribus quantitatis [Master’s Thesis, University of Lisbon]. https://repositorio.ul.pt/bitstream/10451/18435/1/ulfc113829_tm_Tiago_Hirth.pdf

Hua, Z., Xu, B., Jin, F., & Huang, H. (2019). Image encryption using Josephus problem and filtering diffusion. IEEE Access, 7, 8660–8674. https://doi.org/10.1109/ACCESS.2018.2890116

Hutton, C. (1844). Recreations in science and natural philosophy: Dr. Hutton’s translation of Montucla’s edition of Ozanam. Thomas Tegg. https://archive.org/details/b21307507

Klee, V., & Wagon, S. (1991). Old and new unsolved problems in plane geometry and number theory (Dolciani mathematical expositions). Mathematical Association of America.

Loyd, S. (1914). Sam Loyd’s cyclopedia of 5000 puzzles, tricks and conundrums with answers. The Lamb Publishing Company. https://archive.org/details/CyclopediaOfPuzzlesLoyd

Lucas, E. (1891). Récréations mathématiques (vol. 3). Gauthier-Villars et fils. https://archive.org/details/
rcrationsmathma07lucagoog

Martín Pliego, F. J., & Santos del Cerro, J. (2000). Luca Pacioli: en el origen del cálculo de probabilidades. Revista de Historia Económica – Journal of Iberian and Latin American Economic History, 18(2), 405–417. https://doi.org/10.1017/S0212610900008557

Mathematical Association of America. (2023). SIGMAA on recreational mathematics. https://maa.org/member-communities/sigmaas/

Mieg, J. (1839). El brujo en sociedad, ó sea breve instrucción para aprender a ejecutar con destreza muchos juegos de manos y otras varias suertes curiosas y divertidas. Hijos de Catalina Piñuela. http://bdh.bne.es/bnesearch/detalle/bdh0000082676

Ozanam, M. (1778). Récréations mathématiques et physiques. C. A. Jombert. https://gallica.bnf.fr/ark:/12148/bpt6k927336.texteImage#

Singmaster, D. (2021). Adventures in recreational mathematics (vol. I & II). World Scientific.

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Published

2024-03-26

How to Cite

Blasco, F. (2024). Fun sharpens the mind: How simple problems bring us closer to complex mathematical theories. Metode Science Studies Journal, (15). https://doi.org/10.7203/metode.15.27423
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Issue

No. 15: Volume 15 (Online first)

Section

Science anywhere and anyhow. A journey into the fascinating world of recreational science

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