Academic literature on the topic 'Recreational mathematical problems'
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Journal articles on the topic "Recreational mathematical problems"
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Sodhi, Amar. "Discover Mathematical Knowledge through Recreational Mathematics Problems." Mathematics Teacher 97, no. 4 (2004): 258–63. http://dx.doi.org/10.5951/mt.97.4.0258.
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A high-quality recreational mathematics problem should be an intriguing problem that is easy to understand but challenging to solve. If the problem leads each would-be solver to a discovery of myriad ideas in mathematics, then so much the better. An example of such a problem was posed by the Reverend T. P. Kirkman in the Lady's and Gentleman's Diary for 1851 (Kirkman 1850).
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Benson, Steve. "Calendar Problems: January 2004." Mathematics Teacher 97, no. 1 (2004): 40–46. http://dx.doi.org/10.5951/mt.97.1.0040.
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Problems 2–11 and 26–31 appeared in The Contest Problem Book IV: Annual High School Examinations, 1973–1982, compiled and with solutions by Ralph A. Artino, Anthony M. Gaglione, and Niel Shell (Washington, D.C.: Mathematical Association of America, 1983). Problems 12–17 come from Five Hundred Mathematical Challenges, by Edward J. Barbeau, Murray S. Klamkin, and William O. J. Moser (Washington, D.C.: Mathematical Association of America, 1995). Problems 18–23 were taken (or adapted) from problems appearing in the New York City Interscholastic Mathematics League competitions during fall 1977 and spring 1977. Problems 24 and 25 come from Problem Solving through Recreational Mathematics, by Bonnie Averbach and Orin Chein (Mineola, N.Y.: Dover Publications, 2000).
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Antequera-Barroso, Juan Antonio, Francisco-Ignacio Revuelta-Domínguez, and Jorge Guerra Antequera. "Similarities in Procedures Used to Solve Mathematical Problems and Video Games." Education Sciences 12, no. 3 (2022): 172. http://dx.doi.org/10.3390/educsci12030172.
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Video game use is widespread among all age groups, from young children to older adults. The wide variety of video game genres, which are adapted to all tastes and needs, is one of the factors that makes them so attractive. In many cases, video games function as an outlet for stress associated with everyday life by providing an escape from reality. We took advantage of this recreational aspect of video games when investigating whether there are similarities between the procedures used to pass a video game level and those used to solve a mathematical problem. Moreover, we also questioned whether the use of video games can reduce the negative emotions generated by mathematical problems and logical–mathematical knowledge in general. To verify this, we used the Portal 2 video game as a research method or tool. This video game features concepts from the spatial–geometric field that the students must identify and relate in order to carry out the procedures required to solve challenges in each level. The procedures were recorded in a questionnaire that was separated into two blocks of content in order to compare them with the procedures used to solve mathematical problems. The first block pertains to the procedures employed and the second block to the emotions that the students experienced when playing the video game and when solving a mathematical problem. The results reveal that the recreational aspect of video games is more important than the educational aspect. However, the students were not aware of using the problem-solving procedures they learned at school to solve different challenges in the video games. Furthermore, overcoming video game challenges stimulates positive emotions as opposed to the negative emotions generated when solving mathematical problems.
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Crockett, J. A., K. J. Hartley, and W. D. Williams. "Setting and Achieving Water Quality Criteria for Recreation." Water Science and Technology 21, no. 2 (1989): 71–76. http://dx.doi.org/10.2166/wst.1989.0030.
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Water-based recreation is popular in Australia. On the coast many canal estates and marinas are being constructed. Australia's arid and variable climate introduces unusual problems in the establishment of inland recreational lakes. In setting water quality criteria what is achievable must be balanced with what is desirable and criteria may need to be varied between flood and dry periods. Greater emphasis should be placed on understanding, monitoring and managing the ecology of water-bodies. If a stable ecology is maintained, it will generally follow that water quality and conditions surrounding the water-body will be acceptable for human use. In developing new lakes and canals we must carry out some mathematical modelling in order to provide a rational basis for determining water quality criteria and the necessary management actions.
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Heeffer, Albrecht, and Andreas M. Hinz. ""A difficult case": Pacioli and Cardano on the Chinese Rings." Recreational Mathematics Magazine 4, no. 8 (2017): 5–23. http://dx.doi.org/10.1515/rmm-2017-0017.
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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.
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Kovaleva, N., N. Ieremenko, and V. Uzhvenko. "Modern problems of formation of women’s motivation to work in health and recreation movement activities under quarantine restrictions." Scientific Journal of National Pedagogical Dragomanov University. Series 15. Scientific and pedagogical problems of physical culture (physical culture and sports), no. 7(152) (July 30, 2022): 66–69. http://dx.doi.org/10.31392/npu-nc.series15.2022.7(152).16.
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The article is devoted to the substantiation of a set of measures to form the motivation of women to engage in health and recreational physical activity in the conditions of quarantine restrictions. The pandemic in Ukraine has actually reached its peak. For a long time, the population is in a state of constant stress due to the risk of illness, inability to return to the usual rhythm of life, a certain complex of psychological fatigue, formed effective forms of dissemination of information. The purpose of the study is to theoretically substantiate and develop a set of activities that will help increase the level of motivation of women to engage in health and recreational physical activity in conditions of quarantine restrictions. Research methodology - analysis and generalization of special scientific and methodological literature, documentary materials, sociological (questionnaire, expert survey), pedagogical research methods (pedagogical observation, pedagogical experiment), methods of mathematical statistics. Scientific novelty: rhe study of women's motivation to engage in health and recreational physical activity in conditions of quarantine restrictions is relevant. How to motivate women to exercise is an important question today. Successful realization of motivation and goals stimulated the desire of women to continue to show initiative, that is, intrinsic motivation and interest. Conclusions: the proposed program of classes includes 4 sets of activities: setting smart goals, rational use of free time, control of success and promotion, fitness that you like. The variety of means of the offered program allowed to involve women in occupations of improving and recreational physical activity and to promote formation of the positive attitude to a healthy way of life and physical activity.
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Britto, Silvio Luiz Martins, and Malcus Cassiano Kuhn. "Conhecimentos Álgebricos na Seção para Pequenos Mathemáticos da Revista O Echo do Século XX." Jornal Internacional de Estudos em Educação Matemática 16, no. 3 (2024): 343–52. http://dx.doi.org/10.17921/2176-5634.2023v16n3p343-352.
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A questão norteadora deste estudo é quais conhecimentos algébricos estão presentes nos problemas recreativos da seção Para Pequenos Mathemáticos da revista O Echo, publicada na primeira metade do século XX. O artigo tem por objetivo investigar os conhecimentos algébricos envolvidos nos problemas recreativos da seção Para Pequenos Mathemáticos da revista O Echo. Como o tema se insere na História da Educação Matemática no Rio Grande do Sul, este estudo qualitativo e documental se ampara na história cultural para análise das edições da revista, editada pelo Colégio Anchieta de Porto Alegre, no período de abril de 1914 a dezembro de 1931. O público-alvo do Echo era a comunidade escolar e a mocidade católica brasileira, por meio de textos, histórias, informações e curiosidades, enfatizando os aspectos morais, religiosos e a formação em geral. A seção Para Pequenos Mathemáticos fez parte da revista nos anos de 1919, 1920, 1921 e 1924, destacando-se 63 problemas recreativos propostos nessa seção. Esses estão relacionados, principalmente, com conhecimentos de aritmética, álgebra e geometria. Nos problemas recreativos envolvendo conhecimentos algébricos se observaram aplicações de equações do 1º grau, equações irracionais, equações lineares, sistemas com equações lineares, funções do 1º grau, progressões aritméticas e demonstrações de teoremas algébricos. Também envolvem educação financeira, operações comerciais, carreira profissional e comportamento humano. Diante do exposto, observa-se que os editores da revista O Echo buscavam despertar o interesse e a curiosidade da mocidade estudiosa, contribuindo para a formação da juventude católica nos colégios onde essa revista circulava. Palavras-chave: História da Educação Matemática. Educação Jesuítica. Problemas Recreativos. Álgebra. AbstractThe guiding question of this study is what algebraic knowledge are present in the recreational problems of the section For Small Mathematicians of The Echo magazine, published in the first half of the 20th century. The article aims to investigate the algebraic knowledge involved in the recreational problems of the section For Small Mathematicians of The Echo magazine. As the theme if inserted of the History of Mathematical Education in Rio Grande do Sul, this qualitative and documentary study is based on cultural history for the analysis of the editions of the magazine, published by the Anchieta College of Porto Alegre, from April 1914 to December 1931. The audience of The Echo was the school community and the Brazilian Catholic youth, through texts, stories, information and curiosities, emphasizing the moral, religious aspects and the formation in general. The section For Small Mathematicians section was part of the magazine in the years 1919, 1920, 1921 and 1924, highlighting 63 recreational problems proposed in this section. These are mainly related to knowledge of arithmetic, algebra and geometry. In the recreational problems involving algebraic knowledge, applications of 1st degree equations, irrational equations, linear equations, systems with linear equations, 1st degree functions, arithmetic progressions and demonstrations of algebraic theorems were observed. They also involve financial education, business operations, professional careers and human behavior. Given the above, it is observed that the editors of The Echo magazine sought to arouse the interest and curiosity of the studious youth, contributing to the formation of Catholic youth in the colleges where this magazine circulated. Keywords: History of Mathematics Education. Jesuit Education. Recreational Problems. Algebra.
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Melnyk, Andriy, Nadiia Melnyk, Yaroslava Korobeinykova, Olena Pobigun, and Iryna Ierko. "Position of Spain in the global tourism market: its competitive capacity and priorities." Sport i Turystyka. Środkowoeuropejskie Czasopismo Naukowe 5, no. 4 (2022): 135–48. http://dx.doi.org/10.16926/sit.2022.04.08.
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The article is devoted to the study of Spain's place in the world tourism market and determines the specialization of the country's recreational economy. The tourist potential of Spain is characterized. Equal attention is paid to the research devoted to natural recreational resources as well as historical and cultural heritage sites. The role of tourist infrastructure in the development of the country’s tourism sector is outlined. Besides, the paper presents recreational zoning of the territory of Spain. The intensity, dynamics and geography of incoming and outgoing flows, features of domestic tourism, as well as revenues from international tourism and average tourist costs are analyzed. In addition to current data, the dynamics of the main statistical indicators of international tourism are traced. The impact of the global pandemic COVID-19 on the tourism industry of the studied country is estimated. The article depicts the main problems inherent in the Spanish tourism industry, in particular, economic, environmental and social problems. Simultaneously, the main priorities of Spain in the world tourism market are defined. The study was conducted on the basis of analysis of statistical reports and material data of UNWTO and the Institute of National Statistics of Spain, the Alliance for Excellence in Tourism, i.e. Exceltur. The methodological tools of the study involve analytical, statistical, comparative-geo-graphical, mathematical methods, as well as methods of generalization and systematization, etc.
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DMITRIYEV, Pavel S., Ivan A. FOMIN, Jan A. WENDT, Saltanat M. ISMAGULOVA, and Olga S. SHMYREVA. "REGIONAL ASPECTS OF CREATION COMPLEX ROUTES ECOLOGICAL TOURISM ON THE TERRITORY OF NORTH KAZAKHSTAN REGION." GeoJournal of Tourism and Geosites 41, no. 2 (2022): 485–92. http://dx.doi.org/10.30892/gtg.41220-854.
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To consider the possibility of developing ecological tourism in the districts of the North Kazakhstan region of the Republic of Kazakhstan, based on the conducted sociological research and the available natural and recreational potential. The analysis of the conducted sociological survey is given, using methods of statistical and mathematical processing. Visualization of the presented materials was carried out by means of mapping. The study and analysis of the data obtained allowed us to reveal the natural and recreational potential of the studied areas and determine the degree of their demand as objects for tourism development. The results of the sociological survey determined the possibility and necessity of the development of regional ecological tourism, the uniqueness of local natural and recreational facilities by respondents. A cartographic material has been prepared that clearly reflects the opportunities, problems and prospects for the development of the tourism industry in the region. The natural and recreational potential of the territory of the North Kazakhstan region is certainly of interest. Natural and recreational facilities that are potential for the development of the tourism industry in the North Kazakhstan region have been identified on the territory of the studied areas. The border position of the North Kazakhstan region makes it possible for tourists from Russia to visit it. The results of the sociological survey allow us to conclude that the study of the native land has a positive effect on the patriotic education of the younger generation, and is also one of the factors in the development of eco-tourism.
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Schultz, David, and Enrico Serpone. "Sangaku Optimization Problems: An Algebraic Approach." Mathematics Teacher 111, no. 5 (2018): 385–89. http://dx.doi.org/10.5951/mathteacher.111.5.0385.
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During the Edo Period (1603-1867), Japan was isolated from the influence of western mathematics. Despite this isolation, Japanese mathematics, called Wasan, flourished, and a unique approach to present mathematical problems was developed. Painted wooden tablets called sangaku were hung on display at Shinto shrines and Buddhist temples for recreational enjoyment and religious offerings. More than 900 tablets have been discovered with problems developed by priests, samurai, farmers, and children. The vast majority of these problems were solved using analytic geometry and algebraic means, and the collection as a whole is frequently referred to as Japanese Temple Geometry. Within the collection of the sangaku, several optimization problems appear with answers included. However, the methods used to obtain those answers are absent. Because the work of Newton and Leibniz was unknown to the Japanese mathematicians of that time and no evidence exists of contemporaneous Japanese mathematicians having a formal definition of the derivative, their solution techniques to these problems remains unresolved (Fukagawa and Rothman 2008). To illustrate a possible noncalculus approach for the solution to sangaku optimization problems, we will examine two specific examples. To help readers visualize the two examples, Maple™ animations have been created by the authors and can be found at http://www.mesacc.edu/~davvu41111/Sangaku.htm.
Dissertations / Theses on the topic "Recreational mathematical problems"
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Wate, Mizuno Mitsuko. "The works of Kõnig Dénes (1884-1944) in the domain of mathematical recreations and his treatment of recreational problems in his works of graph theory." Paris 7, 2010. http://www.theses.fr/2010PA070079.
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Dénes Kônig est connu comme mathématicien avec ses œuvres importants sur la théorie des graphes. Avant de commencer son travail professionnel, en 1902 et en 1905 quand il était étudiant, il a successivement publié deux livres sur les récréations mathématiques en hongrois, mais ces livres ne sont pas encore beaucoup examinés par des historiens. Dans la présente thèse, j'ai traduit ces livres en anglais, et comparé le contenu avec sa monographie sur la théorie des graphes publiée en 1936. J'ai trouvé que beaucoup de problèmes traités dans le second livre sur les récréations mathématiques de 1905 ont été traités à nouveau dans la monographie de 1936, et que beaucoup de problèmes traités dans la monographie de 1936 ont déjà été traités dans le second livre de 1905. Dans ces deux publications, des mêmes problèmes étaient traités de manières différentes. Pour clarifier les rapports entre les récréations mathématiques et la théorie des graphes, j'ai analysé comment des éléments des diagrammes de la théorie des graphes et des concepts de celle-ci ont été formés dans le contexte de récréations mathématiques. J'ai trouvé que Tarry, dans sa conférence sur la géométrie de situation lors d'un congrès en 1886, a intégré certains concepts de sujets différents de récréations mathématiques, et qu'il a utilisé la même sorte de diagrammes pour examiner des problèmes des sujets différents. Les éléments des diagrammes de Tarry sont similaires à ceux utilisés dans la monographie de Kônig de 1936, et les concepts qui y correspondent peuvent être considérés comme certaines représentations des concepts de la théorie des graphes définis dans la monographie de Kônig de 1936<br>Dénes kônig is known as a mathematician with his important works on graph theory. Before starting professional works, in 1902 and 1905 when he was a student, he successively published two books on mathematical recreations in hungarian, but these books are not yet much examined by historians. In the present dissertation, i translated these books into english, and compared the contents with kônig1s treatise on graph theory in 1936. I found that many problems treated in the second book on mathematical recreations in 1905 were treated again in the treatise 0f 1936, and that many problems treated in the treatise 0f 1936 were already treated in the second book on mathematical recreations in 1905. In these two publications, same problems were treated in different ways. To clarify the relation between mathematical recreations and graph theory, I analyzed how some features of the diagrams 0f graph theory and some concepts of it took shape in the context of mathematical recreations. I found that Tarry, in his talk on geometry of situation in a conference in 1886, integrated some concepts of different topics of mathematical recreations, and that he used the same type of diagrams for considering problems in different topics. The elements of Tarry's diagrams are similar to those used in Kônig's treatise of 1936, and the corresponding concepts can be considered as one of the representations of the concepts of graph theory defined in Kônïg's treatise of 1936
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Anderson, Ebonii Johari. "On a mathematical formulation and solution of the fair-lane assignment problem in bicycle motocross racing." Thesis, 2002. http://hdl.handle.net/1911/17489.
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Bicycle Motocross (BMX) is a sport in which riders compete over an elaborately designed track. The sport of BMX has different systems of qualifying participants to the next round of competition. In the most popular system, a rider has three chances to win a race and advance to the next round. Since lane assigning is traditionally done by three separate random draws, an unlucky rider could be assigned the worst lane each time. This research proposes that choosing lanes for each rider in the beginning as a set of well-structured triples would eradicate this mishap, but calls for a clever method to generate a fair set of triples. A mathematical model and algorithm have been developed that offer an optimal set of triples giving the lane assignment. Therefore, we eliminate the possibility of any rider being victimized by misfortune, and offer each participant an equitable opportunity for advancement.
Books on the topic "Recreational mathematical problems"
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A, Shifman Mikhail, ed. You failed your math test, comrade Einstein: Adventures and misadventures of young mathematicians or test your skills in almost recreational mathematics. World Scientific, 2005.
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I︠A︡shchenko, I. V. Invitation to a mathematical festival. Mathematical Sciences Research Institute, 2013.
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Averbach, Bonnie. Problem solving through recreational mathematics. Dover Publications, 2000.
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Ball, W. W. Rouse. Mathematical recreations & essays. 4th ed. Watchmaker Pub., 2008.
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Kohl, Herbert R. Mathematical puzzlements: Play and invention with mathematics. Schocken Books, 1987.
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Sean, Connolly. The book of perfectly perilous math: 24 death-defying challenges for young mathematicians. Workman Pub., 2012.
Find full textBook chapters on the topic "Recreational mathematical problems"
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Allen, G. Donald. "Problems In Mathematical Recreation." In Pedagogy and Content in Middle and High School Mathematics. SensePublishers, 2017. http://dx.doi.org/10.1007/978-94-6351-137-7_46.
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Banbara, Mutsunori, Kenji Hashimoto, Takashi Horiyama, et al. "Solving Rep-Tile by Computers: Performance of Solvers and Analyses of Solutions." In Algorithmic Foundations for Social Advancement. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-96-0668-9_13.
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Abstract A rep-tile is a polygon that can be dissected into smaller copies (of the same size) of the original polygon. A polyomino is a polygon that is formed by joining one or more unit squares edge to edge. These two notions were first introduced and investigated by Solomon W. Golomb in the 1950s and popularized by Martin Gardner in the 1960s. Since then, dozens of studies have been made in communities of recreational mathematics and puzzles. We first focus on the specific rep-tiles that have been investigated in these communities. Since the notion of rep-tiles is so simple that can be formulated mathematically in a natural way, we can apply a representative puzzle solver, a MIP solver, and SAT-based solvers for solving the rep-tile problem in common. In comparing their performance, we can conclude that the SAT-based solvers are the strongest in the context of simple puzzle solving. We then turn to analyses of the specific rep-tiles. Using some properties of the rep-tile patterns found by solvers, we can complete analyses of specific rep-tiles up to certain sizes, and find new series of solutions for the rep-tiles which have never been found.
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Silva, Jorge Nuno, and Pedro Jorge Freitas. "The Recreational Problems of Tratado de Prática Darysmetica by Gaspar Nicolas, 1519." In Annals of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-21494-3_3.
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Danesi, Marcel. "River Crossing Problems." In Alcuin's Recreational Mathematics. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780198925330.003.0008.
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Abstract The four river crossing problems in Alcuin’s Propositiones—numbers 17, 18, 19, and 20—deal with the fundamental nature of combinatorics, the mathematics of combinatorial structure. They are among Alcuin’s best-known problems. This chapter deals with these problems and their offshoots, including different cultural versions and more complex ones, such as the four-couple version. It also looks at combinatorics more generally, including problems in the field such as Kirkman’s Schoolgirls Problem. River crossing problems exemplify a recurring mathematical archetype—a problem that occurs in other languages and other eras, but with the same mathematical blueprint. The problems have a certain simple logic built into them that does not require any sophisticated training to understand. This may well have been Alcuin’s goal with these problems, showing that mathematical thinking is part of the human brain, manifesting itself in various cross-cultural ways. They are examples of how innate practical knowledge is transformed into theoretical knowledge by the brain, which is at the core of how mathematicians think.
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Danesi, Marcel. "Diophantine Problems." In Alcuin's Recreational Mathematics. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780198925330.003.0006.
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Abstract Solving Diophantine problems involves considering fewer equations than unknowns. The challenge is to figure out the whole numbers that solve all equations simultaneously. There are seven such problems in Alcuin’s Propositiones—numbers 5, 32, 33, 34, 38, 39, and 47. This chapter deals with these problems and the kind of mathematical thinking that they encompass, as well as the kinds of implications they have had for methods of solving equations, including quadratic equations, and for grasping the nature of functions. It is not known if Alcuin had read Diophantus’s Arithmetica, from where such problems originate, but it is clear that he understood the implications that they had for acquiring mathematical skills. Solving Diophantine problems requires acumen and persistence. Alcuin likely included them in his text to challenge his students to think outside the box, thus emphasizing that mathematics requires not only logical thinking but also a large amount of imagination.
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Danesi, Marcel. "Recreational Logic." In Alcuin's Recreational Mathematics. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780198925330.003.0007.
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Abstract There are two problems in Alcuin’s Propositiones, numbers 11 and 14, that fall under the rubric of what today would be called recreational logic. The problems are original to Alcuin, since no earlier versions are known, and may thus be considered to be the founding ones of this puzzle genre. This chapter deals with the implications that these two problems have had not only for recreational logic, but also for studying the relationship between logic and mathematics—an area that has produced an abundance of fascinating ideas, including those by Charles Peirce, Lewis Carroll, Bertrand Russell, and Kurt Gödel, among others. Prominent in bringing out the linkage between logic and mathematical method is the ancient Liar Paradox, which has led to ideas such as the unprovability of certain propositions within systems of logic. What Alcuin seemed to be conveying by including two logic problems in his text, therefore, is that they entail fundamental mathematical thinking, at the same time that they are intellectually entertaining.
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Danesi, Marcel. "Introduction." In Alcuin's Recreational Mathematics. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780198925330.003.0001.
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Abstract Almost everyone has come across the problem of a traveler wanting to cross a river with a goat, a wolf, and a head of cabbage with a boat that can hold only two. This is an ingenious puzzle devised by the eighth-ninth-century scholar and teacher Alcuin of York. It has universal appeal because it taps into an innate sense of mathematical understanding. Alcuin included it in a set of 53 problems, called Propositiones ad acuendos juvenes, which instantly became a classic work in recreational mathematics. This chapter introduces Alcuin’s book in a general way, making a distinction between problems, propositions, and puzzles, and then discussing the nature of recreational mathematics and its relation to mathematical theory and method, as exemplified by Alcuin’s historically important book.
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Danesi, Marcel. "Sequences." In Alcuin's Recreational Mathematics. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780198925330.003.0009.
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Abstract There are two problems in Alcuin’s Propositiones, numbers 12 and 42, that involve the notion of sequences. This chapter deals with these two problems and the many implications they bear. The importance of sequences in mathematics cannot be overemphasized. From ancient paradoxes dealing with infinity, to the Fibonacci Sequence centuries after Alcuin, and the modern theory of infinite sets, the concept of sequence has been a central one in mathematics. It is truly remarkable to note that solving problem 13 involves a sequence based on “2n” as the general term, anticipating several other problems in recreational mathematics, including Lucas’s Towers of Hanoi puzzle in the nineteenth century. The same term has been crucial in many other areas of mathematics, from perfect numbers to Mersenne primes. It is similarly notable that Alcuin’s problem 42 is solved with the exact same kind of method used famously by Carl Friedrich Gauss centuries later. In sum, Alcuin’s two problems dealing with the notion of sequences have borne great mathematical significance.
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Danesi, Marcel. "Countability." In Alcuin's Recreational Mathematics. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780198925330.003.0003.
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Abstract Although Alcuin’s Propositiones was likely intended as a school textbook, many of its problems are important in themselves as ingenious explorations of number properties and methods of countability. This chapter discusses problems 6, 35, 41, and 43 in the text, which embed notions such as exponential growth and decidability, which have become staples of mathematical theory. Also discussed is the notion of cardinality, developed in the nineteenth century by Georg Cantor, who introduced his famous diagonal proof based on a layout of numbers in the form of a sieve. The development of logarithms, the nature of conjectures, and the topic of mathematical impossibility are discussed as well in this. Alcuin’s countability problems show, in microcosm, how mathematics can turn everyday counting problems into abstract knowledge, eliminating the constant need for trial and error.
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Wakeling, Edward. "Recreational mathematics." In The Mathematical World of Charles L. Dodgson (Lewis Carroll). Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198817000.003.0006.
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Dodgson was interested in puzzles and games throughout his life. This chapter concerns a wide range of recreational games and puzzles that he used to inform and entertain his child-friends and his colleagues. Among the topics included are problems involving time, probability, geometry, algebra, and arithmetic, and there are sections on calculating the days of the week, memorizing numbers, testing for divisibility, and on a wide range of other topics. Dodgson compiled puzzles for some of his young friends, and some of these were published in his lifetime (including some that he included in letters to magazines). Others were found in his papers after his death and published subsequently.
Conference papers on the topic "Recreational mathematical problems"
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Ariffin, Muhammad Shahimi, and Azmin Sham Rambely. "Comparison of upper limb muscles behaviour for skilled and recreational archers using compound bow." In THE 4TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES: Mathematical Sciences: Championing the Way in a Problem Based and Data Driven Society. Author(s), 2017. http://dx.doi.org/10.1063/1.4980916.
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Armaidi, Indriana Eko, Hardi Suyitno, and Nuriana Rachmani Dewi. "Implementation of Problem-Based Learning Assisted with Recreation of Second Mathematics to Improve Numeracy and Problem Solving Skills." In International Conference on Science and Education and Technology (ISET 2019). Atlantis Press, 2020. http://dx.doi.org/10.2991/assehr.k.200620.142.
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Zhang, Liping, and Jian S. Dai. "Reconfiguration Mechanism With Interlocking Geometric Constraints From Puzzles." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71488.
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This paper proposes a reconfiguration mechanism modelling for puzzles with its interlocking geometric constraints analysis. Wooden puzzles consisting of interlocking assemebly of notched sticks are often referred to as bar-puzzles, sometime known as the Chinese Puzzles or Chinese Cross. The puzzle with multiple reconfigurable pieces as kinematic links leads to topology arrangements. Although its partition or assembly process can be operated as mechanism motions, there does not appear to be any evidence that the idea of its mechanism property and any configuration analysis originated. To this purpose, this paper set up a static and discrete reconfiguration theory of geometric puzzles for modeling the topology changement as Put Together, Take Apart, Sequential Movement and various others. The partition and assembly process analysis aims to extract the kinematic chains as links and joints. The puzzle unlocking leads to configuration constraints rearrangement problems which accompanying pieces of bars self-grouped as defined reconfiguration links and joints. The mathematical recreation of the mechanism structure stems from its interlocking geometric constraints property. This paper reveals its interlocking property as configuration constraints including many passive constraints and further discloses the mechanism constraints modeling in two different partition methods. The puzzle solutions are first described as reconfigurable topology mechanism and the constrained mobility is analyzed based on an ingenious and distinctive reconfiguration property.