TCC Matemática

URI Permanente para esta coleção

https://repositorio.ifal.edu.br/handle/123456789/50

Navegar

Navegando TCC Matemática por Assunto "Brachistochrone"

Agora exibindo 1 - 2 de 2
  • Imagem de Miniatura
    Item
    Uma abordagem da Cicloide: "a Helena da geometria"
    (Instituto Federal de Educação Ciência e Tecnologia de Alagoas, 2022-01-25) Silva, Jefferson Marinho da; Vasconcelos, Cleverton da Silva; http://lattes.cnpq.br/8600809859832837; Oliveira, Elinelson Gomes de; http://lattes.cnpq.br/4985621981248771; Silva, Tiago Marinho da; http://lattes.cnpq.br/3964717265579881
    This work presents a brief historical research on the cycloid, in addition to an intuitive construction on the curve, working on the definition and parameterization. This research discusses pedagogical practices that link the contents to the playful context of presenting the cycloid and not just algebraic as in calculation books. Taking into account the context of Mathematics, this proposal presents as a problem the lack of interest in the study of the curve, considering that its use was left aside by mathematicians. In the context of these problems, the proposal intends to awaken the relevance of the cycloid, answering the following questions: how to motivate the understanding of the cycloid? How to show practicality through your application? The main objective of the proposal is to present in a more practical way the understanding of the cycloid. This work is based on studies by Boyer (2012), Bustillo and Sassine (2011) and Stewart (2013). With the results, it was possible to observe that although we have other ways to calculate the cycloid, the best way would be with the parametric equations, as they bring us a simpler way of calculating the curve. The results also point to the practicality of building in Geogebra.
  • Imagem de Miniatura
    Item
    Propriedades geométricas e analíticas da família das cicloides: um estudo comparativo
    (2025-07-11) Queiroz, Yasmin Laryssa Lima de Omena; Vasconcelos, Cleverton da Silva; http://lattes.cnpq.br/8600809859832837; Silva, Vanessa Lúcia da; https://orcid.org/0009-0001-9067-8936; http://lattes.cnpq.br/4017185539776065; Souza, Ana Paula Dantas de; http://lattes.cnpq.br/0855037244655705; Costa, Valdir Soares; http://lattes.cnpq.br/0249295123723616
    This work aims to investigate the geometric and analytical properties of the cycloid family, including variations such as the common cycloid, curtate cycloid, and prolate cycloid. The research is conducted through a comparative study that covers both theoretical and practical aspects of these curves, analyzing their parametric equations, derivatives, integrals, and geometric characteristics. Additionally, the study explores historical and contemporary applications of cycloids in contexts such as physics, engineering, and applied mathematics, highlighting classical problems such as the brachistochrone and the tautochrone. The work seeks to contribute to a deeper understanding of these curves from both mathematical and educational perspectives, serving as a resource for teaching differential and integral calculus.