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The Man Who Loved to Count and the Incredible Story of the 35 Camels

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The Man Who Loved to Count and the Incredible Story of the 35 Camels TMAA_A_1221211.3d (Standard Serif) (215£280mm) 16-08-2016 9:57 CE: DK QA: AM JOURNAL OF MATHEMATICS AND THE ARTS, 2016 VOL. 0, NO. 0, 1–9 http://dx.doi.org/10.1080/17513472.2016.1221211 The man who loved to count and the incredible story of the 35 camels Marcio Luis Ferreira Nascimento a,b and Luiz Barcoc Q1 aDepartment of Chemical Engineering, Polytechnic School, Federal University of Bahia, Salvador, Brazil; bInstitute of Humanities, Arts and Q2 Sciences, Federal University of Bahia, Salvador, Brazil; cSchool of Communication and Arts, University of S~ao Paulo, S~ao Paulo, Brazil 5 ABSTRACT ARTICLE HISTORY Q3 In 2015, we commemorated the 120th anniversary of the birth of the brilliant Brazilian mathematics Received 1 May 2015 professor, storyteller and writer, Julio Cesar de Mello e Souza. Under the pen name of Malba Tahan, Accepted 1 August 2016 he published a seminal book on recreational mathematics that has since been translated into many KEYWORDS languages. We reveal the origin of his best-known story, the riddle of the 35 camels to be divided Malba Tahan; recreational 10 among three sons, where the eldest son was to have one-half of them, the second son one-thirdD1 mathematics; 35 camels; and the third one-ninth. This riddle is cleverly solved by adding one camel before dividing them 17 horses; Julio Cesar de amongst the brothers, and then subtracting two camels afterwards. We provide all the solutions to Mello e Souza the more general puzzle in which t jamals (camels) are divided among three brothers ¡ assigning AMS SUBJECT some fraction of the total to each one ¡ by means of adding one camel before dividing and two CLASSIFICATION 15 removing camels after the division is completed. We also address a controversy related to the 97D20; 97D30; 97D40 origins of this type of puzzle. Finally, we conclude that Tahan, the man who loved to count, really existed. 1. Introduction Tahan – a Brazilian mathematics professor, engineer, storyteller and writer named Julio Cesar de Mello e Q4 According to legend, Malba Tahan – whose complete Souza (1895–1974) – and celebrate the 120th anniver- name was Ali Iezid Izz-Edim Ibn Salim Hank Malba sary of his birth. We also reveal the origins, and discuss 45 Tahan – was an Arab writer who was translated into a related controversy, of one of his most well-known 20 Portuguese for Brazilian readers [19,17]. However, in problems: the riddle of the 35 camels. We show all the the first of many curiosities associated with Tahan, his 22 possible ways of dividing the inheritance of t jamals translator, Breno Alencar Bianco, never existed. An (camels) among three brothers ¡ allotting each brother interview with the author who wrote under the pseudo- a fraction of the total ¡ that would permit the introduc- 50 nym of Malba Tahan revealed that Malba means ‘oasisD2’ tion of one, and the subsequent removal of two camels. 25 and Tahan means ‘miller’ (of cereal grain) [5]. His short More specifically, the division of t camels allots 1/a cam- pieces were moral tales and beautiful stories written in els to the older brother, 1/b to the middle brother and 1/ an Arabian style that often touched on mathematical c to the younger brother, with integers a, b, and c satisfy- themes. ing a b c t, and the solutions would provide two 55 These writings were a huge success, and in 1938, remaining camels, after adding just one to the herd. At 30 Tahan published The Man Who Counted (O Homem the end of this paper, we prove that, in addition to being que Calculava)[6], which remains in print in Brazil to a figure of legend, Malba Tahan really existed. this day and has been translated into many languages. Two years later, The Man Who Counted was awarded a prize from the prestigious Brazilian Academy of Letters 2. The Man Who Counted and iD5ts aD6uthor 35 (Figure 1). The story is about a traveller, Beremiz Samir, a Per- Since its first publication in 1938 [6], The Man Who 60 sian mathematician, who joins the narrator on a voyage Counted has been an enormously popular book in Brazil that covers dozens of chapters. On the way our hero elu- and around the world among both mathematics teachers cidates problems using his skills and abilities with num- and general readers. The book is rich in references to 40 bers, puzzlesD4and curiosities. We present a brief overview Islamic traditions and beautiful locations in the Middle of the real man who wrote under the pen name of Malba East and it transports the reader into a magical world 65 CONTACT Marcio Luis Ferreira Nascimento [email protected] Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/17513472.2016.1221211. © 2016 Informa UK Limited, trading as Taylor & Francis Group TMAA_A_1221211.3d (Standard Serif) (215£280mm) 16-08-2016 9:57 2 M. L. FERREIRA NASCIMENTO AND L. BARCO B=w in print; colour online Figure 1. Brazilian Literary Academy prize for The Man Who Counted (O Homem que Calculava). This prize was awarded by the presti- gious Brazilian Academy of Letters (Academia Brasileira de Letras, www.academia.org.br). The certificate reads: ‘1939 Literary Contests; Brazilian Academy Award. In the May 16, 1940 session, MrD3Malba Tahan was conferred the 1939 Tales and Novels Award for writings published in 1938 for his work “The Man Who Counted.” Rio de Janeiro June 29, 1940.’ Source: www.malbatahan.com.br. filled with Bedouins, sheiks, viziers, caliphs, kings, although Tahan later became a person, as will be shown queens, princes and princesses. The mathematical ideas below. Mello e Souza was an engineer and mathematics are simple, gentle, interesting, curiousD7and accessible – professor from Rio de Janeiro, Brazil, who never set foot and they drive each story. Arithmetic and geometric in the Middle East. 70 puzzles abound. Beremiz, the main character, is blessed Born on 6 MayD171895, Mello e Souza chose to teach 90 with a great ability for calculation and elucidates prob- mathematics after completing his engineering degree at lems in mathematics and logic in a wide variety of intri- college, and he wrote short stories in his spare time cate circumstances with great simplicity, talent and [5,6]. He was a professor of civil engineering at the Uni- precision. versity of Brazil, now the Federal University of Rio de 75 This book narrates appealing adventures full of Janeiro (www.ufrj.br). In 1918, the first of his stories was 95 magic, many of which are inspired by Arab legends and submitted to and rejected by the local newspaper, ‘OD18 tales – with myriad references to common terms and ImparcialD19’ (‘TheD20 ImpartialD21’)[5]. Later, he was widely expressions in Arabic, such as Allahu Abkar!(‘AllahD8 is published in Brazil and his columns and recreational the Greatest!D9’), Maktub (‘ItD10 is writtenD1’)D12and Salaam Alai- books typically took the form of a series of tales – ala 80 kum (‘PeaceD13 to youD14’) – and by traditional teachings in The Thousand and One Nights – revolving around math- 100 Arab culture. ematical puzzles, riddles and curiosities. Tahan was born on 6 May 1885,D15 10D16 years before Mello However, it is interesting that Mello e Souza’s first e Souza [18]. However, the book is sometimes consid- attempts to publish his writings were neither easy nor ered a literary hoax because Malba Tahan was a product successful, according to an interview recorded at the 85 of the imagination of Julio Cesar de Mello e Souza – Image and Sound Museum in the city of Rio de Janeiro 105 TMAA_A_1221211.3d (Standard Serif) (215£280mm) 16-08-2016 9:57 JOURNAL OF MATHEMATICS AND THE ARTS 3 (www.mis.rj.gov.br)[5]. Following these initial failures, For example, Wilder et al. [23] proposed an integrated Mello e Souza decided to change the names and places project that merged the teaching standards of mathemat- 160 in his stories, and he resubmitted them to the same ics, social studies and language arts while using technol- newspaper as translations of the ‘incredible’ American ogy as the means for an innovative learning medium 110 writer R. S. Slady, one of the author’s first pseudonyms. for high school students. The product of their efforts, Under this guise, the newspaper printed these first five known as ‘TheD32 Man Who CountedD3’ project, drew inspira- stories – and on the front page! tion from Tahan. Another interdisciplinary project, this 165 After this experience Mello e Souza realized that his one in Portuguese, was proposed and presented by de best chance of success as a writer in Brazil was to use an Faria [5]. 115 Arab pseudonym because, according to Mello e Souza, Arabs had been renowned as great storytellers for centu- ries [5], including the aforementioned The Thousand 3. The rD34iddle of the 35 cD35amels and sD36imilar and One Nights. Thus, his love of mathematics led to pD37roblems Mello e Souza’s fascination with Islamic art and science, fi 170 120 and he decided to write stories about ancient Arabia In the rst occurrence along their journey (Chapter 3 of ‘D38 D39’ under the nom de plume of ‘MalbaD2 Tahan.D23’ This pen The Man Who Counted [19,17], Beasts of burden ), name was first used in the Rio de Janeiro newspaper ‘AD24 Beremiz put an end to a heated inheritance quarrel NoiteD25’ (‘TheD26 NightD27’)inafictitious biography that was between three brothers in the middle of the desert: fi translated by the previously discussed and equally cti- “We are brothers,” the oldest explained, “And we 125 tious Breno Alencar Bianco.
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