Trabalhando com bolas e intervalos: uma abordagem introdutória da topologia
Topology is a branch of mathematics that studies the characteristics and properties of objects and shapes that are maintained even when they are subjected to deformations. Developed from needs that were not answered only with knowledge of Geometry and improved over time with the discoveries of sev...
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| Formato: | Dissertação |
| Idioma: | pt_BR |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/44919 |
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| Resumo: | Topology is a branch of mathematics that studies the characteristics and properties of
objects and shapes that are maintained even when they are subjected to deformations.
Developed from needs that were not answered only with knowledge of Geometry and improved over time with the discoveries of several renowned mathematicians, this branch is
commonly seen in higher education. However, the following thesis was developed in order
to present, in an introductory way, topics in Mathematical Topology that can be treated
and enhanced in high school, considering the limitations of knowledge applied at the level
of education - such as the idea of intervals - and the knowledge already learned during the
student journey. To this end, ways will be presented to introduce Topology ideas, such as
the concept of balls and spheres, through concepts already seen by the students, allying
themselves with concrete examples that can be found in their daily lives. We understand
that the mastery of certain knowledge of the Topology of Metric Spaces brings greater
comfort in dealing with the minutiae of mathematical models involving the line and the
plane. Here, the notion of metrics is approached in a very intuitive way, once students
are already used to the notion of distance between two points, either on the straight or on the plane. |
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