{"title":"Relacionando critérios de divisibilidades com sistemas de numeração","authors":"Thiago Cavalcante, R. Pimenta","doi":"10.21711/2319023x2020/pmo1015","DOIUrl":"https://doi.org/10.21711/2319023x2020/pmo1015","url":null,"abstract":"In this work we are going to relate the divisibility of a number to its numbering system on a given basis. More precisely, we determine when a number written on a given base r is divisible by ( r – 1 ) and ( r + 1 ) . We started from this generalization and obtained the well-known divisibility criteria for 9 and 11, when the number in question is written in the base r = 10. We use these concepts to solve math olympics exercises, graduate questions and unveil some common games in the circles of friends that, the secret answers, are directly linked to numbering systems.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130026356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"O problema de Langley: uma abordagem natural","authors":"J. Ferreira, Fábio de Castro","doi":"10.21711/2319023x2023/pmo1120","DOIUrl":"https://doi.org/10.21711/2319023x2023/pmo1120","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125226175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Grupos diedrais e simetrias da circunferência: uma abordagem geométrica","authors":"Thiarly Souza, A. Guimarães","doi":"10.21711/2319023x2022/pmo1027","DOIUrl":"https://doi.org/10.21711/2319023x2022/pmo1027","url":null,"abstract":"Let D n be the dihedral group, i. e., the group of symmetries of a regular polygon of n sides. In several Abstract Algebra books,","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134369795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Olimpíadas de Matemática: Aritmética e resoluções de problemas","authors":"Manoel Neto, W. Sousa","doi":"10.21711/2319023x2023/pmo1113","DOIUrl":"https://doi.org/10.21711/2319023x2023/pmo1113","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133691775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Equações diofantinas lineares e não lineares: uma abordagem por meio de questões de Olimpíadas de Matemática","authors":"Érick Nascimento, Thiago Tanaka, B. Silva","doi":"10.21711/2319023x2022/pmo1025","DOIUrl":"https://doi.org/10.21711/2319023x2022/pmo1025","url":null,"abstract":"Neste trabalho, apresentaremos m´etodos e t´ecnicas de solu¸c˜ao para equa¸c˜oes diofantinas lineares e n˜ao lineares por meio de quest˜oes de Olimp´ıadas de Matem´atica. No tratamento das equa¸c˜oes lineares, exploraremos a teoria de divisibilidade nos n´umeros inteiros, o conceito de m´aximo divisor comum (MDC) e, ent˜ao, apresentaremos um resultado, provando, assim, a existˆencia de solu¸c˜oes. No caso n˜ao linear, exploraremos t´ecnicas para determinados casos, uma vez que, para equa¸c˜oes diofantinas n˜ao lineares, n˜ao h´a um m´etodo geral de solu¸c˜ao. Apresentaremos quatro casos de resolu¸c˜ao baseados em aritm´etica dos inteiros, fatora¸c˜oes, desigualdades e parametriza¸c˜oes. Espe-ramos que este trabalho sirva como fonte de estudo e pesquisa aos discentes e docentes interessados em Olimp´ıadas de Matem´atica. Abstract In this work, we will present methods and solution techniques for Linear and Nonlinear Diophantine Equations through Mathematical Olympiad questions. In the treatment of linear equations, we will explore the theory of divisibility in whole numbers, the concept of greatest common divisor (GCD) and, then, we will present a result, thus proving the existence of solutions. In the nonlinear case, we will explore techniques for certain cases, since, for nonlinear Diophantine Equations, there is no general solution method. We will present four cases solving based on integer arithmetic, factorizations, inequalities and parameterizations. We hope that this work will serve as a source of study and research for students and teachers interested in Mathematics Olympiads.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115434281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discalculia como transtorno de aprendizagem da matemática: discussão necessária na formação docente","authors":"Alana Alves, Vinicius Varella","doi":"10.21711/2319023x2022/pmo1037","DOIUrl":"https://doi.org/10.21711/2319023x2022/pmo1037","url":null,"abstract":"O transtorno de aprendizagem, diferente do distúrbio, é resultado de uma disfunção na região frontal do cérebro, que causa transtorno no indivíduo. Compromete a atenção seletiva e gera impulsividade, hiperatividade e dificuldade visomotora. O indivíduo com transtorno apresenta comprometimento comportamental aparente.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116156956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sistema de números reais: intuição ou rigor?","authors":"J. Magossi","doi":"10.21711/2319023x2019/pmo75","DOIUrl":"https://doi.org/10.21711/2319023x2019/pmo75","url":null,"abstract":"It is classic that some ideas present in courses of Calculus go back to Antiquity, since Archimedes, who, among other scientists, also debated the existence of the continuum. This problem was addressed by I. Newton and G.W. Leibniz, who, in the seventeenth century, developed the Calculus. But geometric intuition, as early as the eighteenth century, did not solve problems of “continuity” that presented themselves to mathematicians. B. Bolzano, A. L. Cauchy, K. Weierstrass, and R. Dedekind questioned the foundations and began the era of rigor in mathematics, whose North turns out to be the system of real numbers: a complete ordered body. A diagnosis in current books of Calculus shows us that intuition and rigor merge, whether in definitions or in demonstrations. This may create doubts for the less attentive reader. The objective is to present a scenario in which geometric intuition reveals pedagogical strategies and rigor indicates the need for mathematical precision.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121173119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"O Teorema Japonês para polígonos cíclicos convexos","authors":"Italo Vieira Jr, F. Souza","doi":"10.21711/2319023x2021/pmo942","DOIUrl":"https://doi.org/10.21711/2319023x2021/pmo942","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116415704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Técnicas para resolução de equações Diofantinas lineares","authors":"Egidio Filho, M. Rodrigues, Orlando Eduardo Ferri","doi":"10.21711/2319023x2022/pmo101","DOIUrl":"https://doi.org/10.21711/2319023x2022/pmo101","url":null,"abstract":"Different mathematical strategies can be used to solve the same problem and it is salutary that the student experiences multiple techniques for facing problem situations, thus understanding that mathematics is dynamic. Based on this premise, this paper brings a study of linear Diophantine equations presenting three resolution strategies, in which two of them have in essence the theory of the greatest common divisor between two integers and the other deals basically with successive divisions.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131790846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sobre como Arquimedes obteve suas aproximações 223/71 e 22/7 para o número 0: uma abordagem histórica","authors":"Márcio Albertino, Humberto Bortolossi","doi":"10.21711/2319023x2021/pmo935","DOIUrl":"https://doi.org/10.21711/2319023x2021/pmo935","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128780786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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