PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matematica
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Item A matemática da música: uma possibilidade para o ensino-aprendizagem(Universidade Federal de Goiás, 2023-11-29) Oliveira, Jéfferson Neres; Santos, Ronaldo Antonio dos; http://lattes.cnpq.br/9663485072140551; Santos, Ronaldo Antonio dos; Gomes, Alacyr José; Batista, Marcos RobertoIn our society, Mathematics and Music often hold opposing positions. While the former is associated with suffering, difficulty, and, for some, even elicits repulsion, the latter is a source of enjoyment and happiness, consistently linked with feelings of pleasure and well-being. Although seemingly at odds when we consider about the sensations that each one evokes within us, music and mathematics share profound connections. In this work we study and explore these connections with the aim of gaining a deeper understanding of the history and theoretical underpinnings of music. Additionally, we propose contributions related to this subject to enhance the teaching and learning process, making it more meaningful. We believe that the most effective way to fully leverage the connections between music and mathematics is through the use of an Active Methodology. The type of methodology we chose was problematization, which presents a logical sequence that involves collecting data, raising hypotheses, discussions, experiments, reaching the synthesis and consolidation of this knowledge, and even the generalization of results. In this sense, we present proposals that involve the contents of ratios, proportions, directly and inversely proportional quantities, logarithms, operations with radicals, and trigonometric functions. We emphasize that the proposals do not aim to teach the mentioned contents from the beginning but rather to deepen these concepts, promoting more meaningful learning. The proposals we present aim to emphasize mathematics' capacity to extend into various other fields, typically aiding in the comprehension of the specific characteristics of those domains and offering tools for their systematization. This characteristic has often been overlooked in the context of mathematics teaching and learning.Item Ajuste de curvas usando métodos numéricos(Universidade Federal de Goiás, 2018-06-28) Sousa Neto, Theófilo Machado de; Vieira, Ewerton Rocha; http://lattes.cnpq.br/9011778118531233; Vieira, Ewerton Rocha; Andrade, Kamila da Silva; Lima, Dahisy Valadão de SouzaGiven the need to discuss mathematical methods capable of adjusting curves that represent experimental data. This work presents seven methods of curves adjustment, three of these, methods that use least squares regression techniques and the other four, using interpolation techniques. Initially, it brings some definitions that present to the reader all the mathematical foundation that rules the equations. In parallel, it seeks to discuss, through examples, the area of attribution of the described methods, realizing whenever possible a comparation between the several techniques presented and their errors in the estimates. In order to demonstrate that the techniques discussed here are feasible for use in basic education, it exposes an experience of applying one of these methods in solving a basic problem of the discipline of Physics. After presenting the step-by-step method of obtaining soil resistivity, a variable that is of the utmost importance for the elaboration of projects for grounding meshes that supply energy substations, We finish this work by solving the problem with the aid of adjustment techniques curves studied, proposing the inclusion of the methods addressed in one of the steps of the procedure to obtain soil resistivity.Item A álgebra dos polinômios(Universidade Federal de Goiás, 2020-05-28) Sousa, Reginaldo Jacinto de; Dias , Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias , Ivonildes Ribeiro Martins; Martins, Ivonildes Ribeiro; Assis, Aline Mota de MesquitaIn this work, we will approach the definition of polynomial using the concept of sequence, which allows you to remove the ambiguity from the symbol x, and we will study the algebraic structure of the polynomial rings, the concept and criteria of polynomial irreducibility and factoring of a polynomial in the product of irreducible polynomials, aiming to provide mathematics teachers who work in high school, a deepening in the study of abstract algebra. Obtaining, some suggestions of applications in the classroom, for example, the study of the rationality of a given number.Item Algoritmos utilizados para as quatro operações elementares(Universidade Federal de Goiás, 2016-09-26) Santana, Gracielly da Silva; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Dias, Ivonildes Ribeiro Martins; Vasconcelos, José Eder Salvador deThis work is meant to study some properties of the four elementary operations on the set of natural numbers. Some relevant aspects to Decimal Numbering System will be verified as well as the expansion of a number on that system. It will also demonstrate the usage of the "Golden Beads", a very useful pedagogical resource when it comes to understanding the Decimal Numbering System and even its usage to solve one of the elementary operations. Therefore, some of the algorithms that can be used to solve each of the four operations: addition, subtraction, multiplication and division.Item Análise combinatória: uma questão de lógica e linguagens(Universidade Federal de Goiás, 2013-03-01) Alvim, Karina Guerra Cardoso; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Seimetz, Rui; Vieira, Elisabeth Cristina FariaThe objective of this work is to address the Combinatorial Analysis as a theme that can be treated in the classroom, without the utilization of mathematical formulas in problem solving. For this it will presented a method of reasoning that, basing on logic and languages, underscores the importance of: To read, interpret and analyze texts that are presented in the mother tongue; Formulate conjectures, make choices and seek strategies of count; and Make the correct translation between languages maternal and mathematics. Expected to show from this approach that the Combinatorial Analysis, besides its importance in various elds of knowledge, may also be seen by students and teachers as a challenging and stimulating content.Item Análise do discriminante em equações polinomiais de terceiro grau a partir de funções simétricas(Universidade Federal de Goiás, 2020-11-09) Costa, Debora Naiure Araujo; Gomes, Alacyr José; http://lattes.cnpq.br/5994366998164007; Silva, Geci José Pereira da; Belisário, Hugo Leonardo da Silva; Gomes, Alacyr JoséThe objective of this work is to make a study on the characteristics of the roots of polynomial equations of degrees 2 and 3, studying the discriminant written in function of invariants that depend only on the coefficients of an initial equation. We will start by remembering some important definitions and propositions about polynomials, symmetric functions of the roots and develop the resolution of the cubic by radicals using two different methods. Finally, it will be possible to analyze the discriminant through algebraic manipulations that we will do, using the content presented in the previous chapters, and then we will write the discriminant from the roots of the equations, which enable to develop a proof for the theorems that relate the roots of the equations 2º and 3º degrees with their discriminants.Item Uma análise sobre as novas modalidades de financiamento imobiliário(Universidade Federal de Goiás, 2020-06-16) Barra, Willian do Amaral; Lemes, Max Valério; http://lattes.cnpq.br/6512955169729670; Lemes, Max Valério; Moreira, Fernando Ricardo; Lourenço, Kélem GomesThis dissertation presents a discussion on the importance of Financial Mathematics and Financial Education in relation to practical everyday situations, such as when contracting real estate financing. In August 2019, a decision by the National Monetary Council changed the rules for contracting real estate financing, with this, new financing modalities emerged. We will perform some simulations of real estate financing comparing the current modalities, assessing the advantages and disadvantages of the credit lines offered. To support the discussions on financing, we will present some concepts and examples related to financial mathematics, such as interest rates, compound capitalization system, uniform series and amortization systems. Concepts and laws that regulate the real estate financing system will be presented in order to assist the reader in making strategic decisions.Item Uma aplicação da congruência na determinação de critérios de divisibilidade(Universidade Federal de Goiás, 2015-03-27) Silva, Luis Henrique Pereira da; Souza, Mário José de; Souza, Mário José de; Cecconello, Moiseis dos Santos; Lima, Lidiane dos Santos MonteiroThis work aims to demonstrate in a practical way the divisibility criteria 2-97 in sieve Eratostenes with cutting the right and the left, based on the method of multiplication and division Egyptian. The entire process is demonstrated using the divisibility to whole numbers, greatest common divisor, prime numbers, decomposition in prime factors and matching.Item Aplicação do mínimo múltiplo comum generalizado nas ondas de pêndulos(Universidade Federal de Goiás, 2016-03-30) Silva, Jean Carlo de Sousa e; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Smith, Ole Peter; Vasconcelos, Jose Eder Salvador deThe simple pendulums have oscillatory and periodic movements. Thus, if we analyze some of them with independent movements, they may again return to be in the same spot, if your periods are comensurávies. We present the basic concepts needed to understand this phenomenon. Ending with a hint of implementation.Item Aplicação do polinômio de Taylor na aproximação da função Seno(Universidade Federal de Goiás, 2014-07-03) Curi Neto, Emilio; Silva, Maxwell Lizete da; http://lattes.cnpq.br/9078818338290451; Silva, Maxwell Lizete da; Silva, Sílvia Cristina Belo e; Tonon, Durval JoséIn this work the main goal is focused on applying the theory of Taylor polynomial approximations applied on the trigonometric function defined by f : [0; 2 ] ! R, where f(x) = sin(x). To achieve this goal, eight sections were developed, in which initially a reflection on the problem and the need to obtain the values in this respect in that it is wide angle measure x is presented. Is presented and subsequently treated a problem involving the movement of a pendulum, which uses the approximation sin(x) x where x belongs to a certain range. In the sections that follow a literature review of the theories of differential and integral calculus is presented, and the related theory of Taylor approximation of functions by polynomials. Later we used these theories to analyze and determine polynomials approximating the function f(x) = sin(x) in a neighborhood of the point x = 0, and estimate the error when we applied these approaches. At this time the error occurred due to the approach used in the pendulum problem was also analyzed. Finally a hint of practice to be held in the classroom using the theories treated here as well as the study of the problem of heat transfer in a bar through the theory of Fourier activity is presented.Item Uma aplicação web como recurso didático em aritmética(Universidade Federal de Goiás, 2020-03-13) Lima, Felipe Viterbo de; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Leandro, Bianka Carneiro; Lima, Thaynara Arielly deIn this work, we aim to show the efficiency brought by a given web application that was developed with the purpose of serving as a pedagogical resource, in the mathematics teaching, specifically arithmetic. The conclusions of the present study come from the analyzes carried out and the results obtained during the period of experimentation of this application. Here will be described in detail the functionalities existing in this software, how it was disseminated and how the evaluation made by its users will also be presented. In order to have a good understanding of the mathematical context involved in this dissertation, it is worth mentioning that its target audience is composed of students and teachers who already have knowledge of the main basic concepts related to the arithmetic theory of numbers.Item Aplicações das transformações conformes em problemas eletromagnéticos(Universidade Federal de Goiás, 2014-07-11) Cunha, Ricardo Ferreira da; Calixto, Wesley Pacheco; http://lattes.cnpq.br/9073478192027867; Mota, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539; Mota, Jesus Carlos da; Alves, Aylton José; Calixto, Wesley Pacheco; Silva, Maxwell Lizete daIn this work we describe soem properties of the complex numbers and analytical functions. As an application, we use the conformal transformations to caculate analytical solutions for electromagnetic problems defined in nonconventional domain. The conformal transformation are of excepcional importance in solving boundary value problems in electromagnetic theory. The conformal transformation have the property of modifying the geometry, but preserving the pysical quantities.Item Aplicações do princípio de Cavalieri ao cálculo de volumes e áreas(Universidade Federal de Goiás, 2013-02-28) Lula, Kariton Pereira; Chaves, Rogerio de Queiroz; http://lattes.cnpq.br/2029572406153004; Chaves, Rogerio de Queiroz; Souza, Flávio Raimundo de; Silva, Rosângela Maria daIn elementary mathematics teaching, it often occurs that some subjects are presented without proper justi cation or without a coherent logical construction that makes sense of those subjects and ideas in a wider context. The calculation of areas and volumes is an example of a subject in which these shortcomings are usually present. In this work, we present a model for the gradual development of the ideas involved in the calculation of volumes, in a way that is, at once, well justi ed and approachable by the average student at this stage. In order to achieve that, we make extensive use of the Cavalieri Principle, which allows not only an adequate justi cation of the expressions for the volume of cylinders, cones or spheres, but also the calculation of volumes of other shapes, such as parts of the sphere, ellipsoids and paraboloids. We conclude with an interesting application of the Cavalieri Principle to calculate the area of a parabolic segment and then give a demonstration of Archimedes' theorem.Item Aplicativos educacionais como ferramentas no ensino da matemática(Universidade Federal de Goiás, 2021-10-19) Gama, Bruno Nogueira Gonçalves; Lourenço, Kélem Gomes; http://lattes.cnpq.br/6219440124523685; Lourenço, Kélem Gomes; Silva, Sunamita Souza; Alvarenga, Karly BarbosaThis research pursued to investigate and develop proposals for the use of educational applications as learning facilitators. Society has been increasingly dealing with new technologies, and its popularization results to children and teenagers being connected at all times. Therefore, the reflection of the new generation of students in a digital world motivated this work. This research was developed through a bibliographic gathering, curricular parameters analyses and introduction of mathematical applications for touchscreen devices. The math problems introduced, solved with the help of applications, approached models constantly appeared in college entrance exams, Math Olympiads and in textbooks, this choice shows the concern to demonstrate wide use of the educational tool researched. It was observed that the applications proposed can promote the students’ interest in learning mathematics and instruct teachers on new possibilities for educational tools.Item A aprendizagem da Matemática pela pessoa com síndrome de Down(Universidade Federal de Goiás, 2019-03-25) Fonseca, Claudiney da Silva; Santos, Maria Bethânia Sardeiro dos; http://lattes.cnpq.br/9592720615600301; Santos, Maria Bethânia Sardeiro dos; Faria, Elisabeth Cristina de; Dalla Déa, Vanessa Helena SantanaThe present work deals with an exploratory study about Down Syndrome and the mathematical learning of these individuals. Throughout the work we have tried to answer simple questions, but of competing answers: “When we receive a student with Down syndrome in the classroom, what should we do ? - “ what should we know about him/her?” - “Where do we seek help, and how we should teach ?” - “ Will he/she be able to learn?”Item Aprendizagens construídas, aprendizagens percebidas: caminhos percorridos no trabalho de mediação com objetos de aprendizagem(Universidade Federal de Goiás, 2019-10-29) Soares, Duciclea Amorim; Faria, Elisabeth Cristina de; http://lattes.cnpq.br/5007480938176936; Faria, Elisabeth Cristina de; Silva, Jhone Caldeira; Teixeira, Ricardo Antônio GonçalvesThis research aimed to investigate the learning that is identified by employing Learning Objects (LOs) through the smartphone to teach polynomial function of the 1st degree. As support for the research, a digital book was elaborated through GeoGebra, structured from the combination of videos, games, simulators and applications, aiming to explore several concepts of polynomial function of the 1st degree. From the perspective that learning occurs through student interaction with the environment, we adopted as main references: Oliveira (2001), Moran et al (2017) and Moysés (2012). The LOs were applied in twelve meetings to a group of students from the first grade of a high school of a public school in the interior of Goiás and for data analysis, we observed the ways the students interacted with the LOs; the kinds of difficulties that arose; the interactions: student-OAs; student-student and student-teacher, watching when they occurred and how they occurred; the identified learning and the potentiality of the LOs as an auxiliary resource for the cognitive process. It was possible to identify that, through OAs, the students showed a greater engagement during the class, especially when working on the concepts of functions through games and spreadsheets. The reduced screen of the smartphone did not represent an obstacle to the performance of activities and the use of LOs associated with the teacher's role, as a facilitator and motivator in the mediation relationships established in the research scenario, proved to be important to establish a relationship of trust. between the mediator and the mediator, presenting positive results in the students' learning.Item Aritmética com Python(Universidade Federal de Goiás, 2018-10-11) Cavalcante, Rogério da Silva; Lima, Thaynara Arielly de; http://lattes.cnpq.br/3324489027928883; Lima, Thaynara Arielly de; Rodrigues, Eunice Cândida Pereira; Smith, Ole PeterWe aim to show how effective the technological resources can be when used for teaching. We chose to use the Python programming language in mathematics teaching, specifically arithmetic, showing how logic moves naturally between computing and mathematics, thereby showing a natural interdisciplinarity between these subjects. We propose programs built from the demonstrations of some classic results of arithmetic, aiming to integrate the teaching of these results to the teaching of basic tools of a programming language.Item Aritmética modular: uma aplicação no ensino fundamental(Universidade Federal de Goiás, 2018-05-15) Pinheiro, Rodolfo Cavalcante; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Oliveira, Ricardo Nunes de; Silva, Sílvia Cristina Belo eThis paper presents a proposal to work with Modular Arithmetic with elementary students II (6th, 7th, 8th and 9th years) in order to make the teaching of mathematics more in depth and to get rid of textbooks. We present a sequence of contents that begins in the prime and compound numbers, discusses the meanings of multiples, divisors (and the remainders of divisions) and divisibility rules. To develop the Modular Arithmetic theme we are still exploring the definitions of Diophantine Equations. We conclude by showing the applicability of the theme to the study of Cryptography (Caesar cipher and RSA method). The work still brings results of the application of the project carried out with a specific group of students in a private school in the state of Goiás.Item Aspectos históricos e teóricos das loterias(Universidade Federal de Goiás, 2013-10-01) Freitas, Mateus Almeida de; Santos, Fabiano Fortunato Teixeira dos; http://lattes.cnpq.br/6866594296187427; Santos, Fabiano Fortunato Teixeira dos; Souza, Flávio Raimundo de; Souza, Marcelo Almeida deHistorical Aspects of Theoretical and Lotteries begins with the historical context of gambling; shows examples of such games, such as launching a data or existing machines in casinos, brings Article 50 of Law 3688 of October 3, 1941 (which de nes what is considered gambling), shows curious facts involving games such as the construction of the GreatWall of China, starting around 221 BC, and was partly funded by lottery, said the beginning of the lotteries in Brasil, which occurs during the colonial period, more precisely in Minas Gerais. The paper also presents the evolution of the lotteries, 1784 until our present day and is two games o ered by lotteries Brazilian telling some stories. This work has a mathematical approach , with applications aimed at adds universe of lotteries, in particular two products o ered by the lotteries box: Mega-Sena and Quina. Two methods for generating random numbers present some applications to generate random sequences in simulation betting results.Item Batalha naval e suas aplicações(Universidade Federal de Goiás, 2016-05-30) Soares, Vanessa Ribeiro; Lima, Lidiane dos Santos Monteiro; http://lattes.cnpq.br/3020743359147341; Lima, Lidiane dos Santos Monteiro; Vasconcelos, José Éder Salvador de; Dias, Ivonildes Ribeiro MartinsThis work has the purpose contribute to the improvement in some teaching contents of analytic geometry and trigonometry in high school . The content work was based on the National Curriculum Parameters, highlighting de nitions, theorems and properties necessary for the development of student learning. The theme was chosen after a practical experience involving the Naval Battle game in order to reduce the students' di culties. The playful work, as the game, has a practical application that does the student become familiar with the content. That's an interesting way to propose problems and solutions involving the content. Thus becomes something attractive to the student and encourages creativity in nding problems solutions.