TCC - Licenciatura em Matemática (Sede)
URI permanente para esta coleçãohttps://arandu.ufrpe.br/handle/123456789/466
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Resultados da Pesquisa
Item Sequência de Lucas e suas conexões com a Sequência de Fibonacci(2025-03-14) Nascimento, Christiana Granja do; Cruz, Thamires Santos; http://lattes.cnpq.br/1040714627056870; http://lattes.cnpq.br/2075180354251759Este trabalho tem como foco o estudo das relações entre as sequências de Fibonacci e Lucas, com ênfase nas propriedades e aplicabilidades da sequência de Lucas no ensino básico. A sequência de Fibonacci, amplamente reconhecida por suas aplicações em diversos campos da matemática, possui conexão com a sequência de Lucas, que compartilha a mesma relação de recorrência, mas apresenta características que facilitam a compreensão de algumas identidades, tornando-a interessante para o aprendizado de sequências no contexto educacional. Neste contexto, é explorada a relação entre essas sequências e as raízes de uma equação quadrática, derivada do Teorema de Kepler. Além disso, esse estudo abrange também resultados históricos, como as fórmulas de Binet para ambas as sequências e identidades algébricas relacionadas. Mais ainda, são abordadas as potenciais contribuições da sequência de Lucas no desenvolvimento do raciocínio matemático e na introdução de conteúdos de sequências no ensino básico.Item A técnica de simulação de Monte Carlo aplicada ao cálculo de áreas no ensino médio(2025-01-31) Araújo, Roberta Elaine Domingos de; Barros, Kleber Napoleão Nunes de Oliveira; http://lattes.cnpq.br/1338915220161592; http://lattes.cnpq.br/6420618435459342This study presents the application of the Monte Carlo integration technique for calculating areas of plane figures, aiming to enhance Mathematics education in high school. The methodology includes a practical and experimental approach, involving computational simulations using R software and engaging classroom activities, such as the use of tangible materials to estimate areas of geometric shapes. The theoretical framework encompasses concepts from geometry, probability, and statistics, providing a solid foundation for the method’s application. The results indicated that the use of the Monte Carlo technique improved students’ understanding of mathematical concepts and increased their interest in the subject. Additionally, it was observed that increasing the number of random samples enhances the precision of the estimates, validating the method’s effectiveness. It is concluded that integrating interactive practices and computational tools into teaching enables more meaningful and contextualised learning, making it a valuable strategy for various educational levels.Item A Transformada de Fourier: da motivação à equação do calor numa barra infinita(2024-10-02) Basilio, Evellyn Karoline Alves Freitas; Freitas, Lorena Brizza Soares; http://lattes.cnpq.br/2302580820419163; http://lattes.cnpq.br/8020476628705052This paper presents an overview of the Fourier Transform, its properties and applications, with a particular emphasis on the space of rapidly decreasing functions, which is known as the Schwartz space. The Fourier transform is a fundamental tool in mathematical analysis, employed for the resolution of partial differential equations. This enables differential equations to be converted into more readily manageable algebraic equations. The methodology adopted is based on an analysis of the Schwartz space and its properties, which are essential to ensure the proper behavior of functions in the context of the Fourier transform. Subsequently, the principal properties of the Fourier Transform are examined, including its linearity, differentiability and applicability within the context of Schwartz space, as well as its inverse transform. This work was developed based on an investigation of bibliographical references and theoretical materials listed at the end of this paper. The results obtained demonstrate the significance of the Fourier Transform in determining the solution to the heat equation in an infinite bar, thereby facilitating the identification of a potential solution for the associated partial differential equation. It is our intention that this work provides a clear and comprehensive overview of the Fourier Transform, its properties and its theoretical applications, thus establishing it as an essential tool in analysis.Item Equações polinomiais do I ao IV grau: uma breve história do seu desenvolvimento(2024-10-02) Santos Neto, José Pio dos; Souza, Cícero Monteiro de; http://lattes.cnpq.br/7540654793551489; http://lattes.cnpq.br/5113765752328533The present work aims to present a History of Algebra, with an emphasis on the evolution of concepts and the formalization of polynomial equations from the first to the fourth degree, as well as to analyze the solution methods developed over time. Initially, the algebraic contributions of primitive civilizations are presented chronologically, covering the crucial moment of the systematization of mathematics by the Greeks until the fall of the Roman Empire. Then, with the arrival of the Middle Ages, the Arab invasions, the establishment of the House of Wisdom, and the translation centers, mathematics became accessible to all peoples, and consequently, algebra began to gain significant importance in problem-solving, especially in commercial transactions. By the end of the Middle Ages, first- and second-degree algebraic equations could already be solved, although negative roots were still not considered. Finally, in the 16th century, the concept of imaginary roots and the solution of third- and fourth-degree equations were developed. However, it was only with the French mathematician François Viète (1540 – 1603) that algebra began to evolve into modern algebra, with the creation of a literal notation for the representation of numbers, whether known or unknown, through letters.Item A utilização da robótica como alternativa para o trabalho com comprimento da circunferência e ângulo(2019-07-24) Assis, Pablo Oliveira de; Costa, Wagner Rodrigues; http://lattes.cnpq.br/7087770599703498Math teachers often realize kids struggle about geometry and units of measurement. specifically, about angles and circumference applications. This article shows how these concepts can be explored using the educational robotic to reach an active learning over a teacher supervision. For this research we invited 6th grade students and the data showed that association with mathematics concepts and technology made it easier to think about math and use it to solve problems.Item O floco de neve de Koch e suas propriedades: funções contínuas sem derivada em ponto algum(2024-07-31) Santos, Vivian Maria dos; Clemente, Rodrigo Genuino; http://lattes.cnpq.br/4351609162717260; http://lattes.cnpq.br/0771390443429539In this work, we present the existence of real continuous functions that have no derivative at any point. For this, we use the function developed by the mathematician Helge von Koch as an example, demonstrating that this function is continuous at all points but not differentiable at any point. We show how this curve is constructed and discuss itsproperties. To highlight these facts, many constructions of such functions are based on infinite series of functions. Therefore, we introduce some fundamental concepts and results from Mathematical Analysis, specifically, Sequences and Series of functions, which allow us to investigate the continuity and differentiability properties. Finally, we will comment on an interesting result that reveals that the set of these functions constitutes a dense and residual set in the complete metric space, meaning that these functions exist abundantly. The proof of this statement is based on Baire’s Theorem, which generally states that any countable union of thin sets is so small that its complement is dense.Item Geometria na OBMEP: uma análise de questões da primeira fase do nível 2 à luz da BNCC(2023-09-20) Silva, Luiz Guilherme Machado e; Barboza, Eudes Mendes; http://lattes.cnpq.br/9426464458648172; http://lattes.cnpq.br/0988088024884324The Brazilian Mathematical Olympiad for Public Schools (OBMEP) is applied nationally and reaches a large proportion of Brazilian students. Thinking about it, this work aims to carry out a data survey, in order to clarify which are the skills of the National Common Curricular Base (BNCC) of the thematic unit of Geometry that have more recurrence in OBMEP. For this, the questions dealing with Geometry at OBMEP, level 2, 1st phase, between the years 2017 and 2022 were analyzed.It is worth noting that in the years 2020 and 2021 there were no applications of the tests due to the Covid-19 pandemic. Thereby, this work is a facilitator material for teachers who seek to work Geometry in the classroom using Olympic questions and also for students who intend to participate in Mathematics Olympics.Item Um estudo comparativo entre espaços vetoriais normados de dimensão finita e infinita(2022-06-09) Carvalho, Yasmin Lopes de; Barboza, Eudes Mendes; http://lattes.cnpq.br/9426464458648172; http://lattes.cnpq.br/5996127469682998Vector spaces are structures in which we can add elements and multiply their elements by scalars. When a vector space is provided with a norm, we can also verify metric and topological properties. In Linear Algebra, we study important results that hold for finite-dimensional vector spaces. However, we cannot always extend these results to infinite-dimensional normed vector spaces. With the help of Linear Algebra, Metric Spaces and Functional Analysis, we will see basic notions and enough tools to discuss some differences between normed vector spaces of finite and infinite dimensions. The differences we’ll see are related to norms, linear transformations, completeness, compactness, and closed vector subspaces. We will show valid results for finite dimensional spaces and present examples and counterexamples to show that such results are not always valid in infinite dimensions.Item Bingo Pitagórico: um recurso didático para o estudo do teorema de Pitágoras com estudantes surdos(2024-03-07) Oliveira, Izadora Matilde de; Espíndola, Elisângela Bastos de Melo; Marques, Rafael Emil Korossy; http://lattes.cnpq.br/7531969835893918; http://lattes.cnpq.br/0367382856462792; http://lattes.cnpq.br/6855272795384830This research aims to analyze the use of the "Pythagorean Bingo" as a didactic resource to promote the understanding of deaf students of the 1st year of High School about the Pythagorean theorem. For this, we took as theoretical support research on the teaching of mathematics to the deaf. The research was carried out with 12 deaf participants, students of a public school in Recife-PE. Data production occurred in three stages. In the first, we made a diagnosis about the students' difficulties in Mathematics and especially about the Pythagorean theorem. In the second, we aim to explain how to calculate the measurement of one of the sides of the right triangle in order to prepare students for the use of the game. In the third stage, we applied a questionnaire for the students to give their opinion on the activities that were carried out in the previous stages. The results indicate that the students had a good development in the understanding of the Pythagorean theorem with the realization of the game. This reveals clues about the need for more research on games and other didactic resources for teaching Mathematics to deaf people in the final years of Elementary School and/or High School.Item Da propagação do calor à construção de desenhos: uma aplicação das séries de Fourier com Python(2024) Domingos, Cleianderson Paz; Freitas, Lorena Brizza Soares; http://lattes.cnpq.br/2302580820419163; http://lattes.cnpq.br/8909785797719318This work aims to present an application of Fourier series in generating figures. To do so, we first study the problem of heat conduction in a finite rod, as well as the equation that models it and its solution, both proposed by Joseph Fourier in the early 19th century. Initially, a historical note is presented, exhibiting some facts that lead to the motivation for studying heat propagation. Then, we derive the Heat Equation from two physical laws and study how Fourier series emerge in an attempt to solve this equation. Subsequently, through convergence theorems, we study necessary conditions for a function to be represented by its Fourier series. Finally, we explore an application of Fourier series in figure generation using epicycles and develop a Python algorithm to visualize this application.