A geometria fractal para o ensino de diversos tópicos de matemática no Ensino Médio
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Data
2022-01-21
Autores
Souza, Soraia Perez de
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Universidade Estadual Paulista (Unesp)
Resumo
O presente trabalho tem como objetivo utilizar a Geometria Fractal como motivadora no ensino de áreas e perímetros de figuras geométricas Euclidianas. Além disso, com o intuito de contribuir para um ensino mais prazeroso e dinâmico da Matemática aliado ao uso das tecnologias propõe-se, por meio do Software Geogebra a criação de atividades a serem desenvolvidas no contexto da sala de aula do Ensino Médio no desenvolvimento de conceitos matemáticos como Progressão Geométrica, Geometria, Trigonometria, Logaritmo e noções de limites entre outros temas. Apresentam-se os fractais clássicos : Tapete de Cantor, Tapete de Sierpinski, Ilha de Koch, Esponja de Menger, Fractal Hexagonal de Dürer, Fractal Octagonal de Dürer e os fractais circulares: Fractal Circuntexto , Fractal Tetracírculo, Fractal Antena Circular, Fractal Peneira de Apolônio e Fractal Flor da Vida. Concluí-se que a Geometria Fractal possibilita ao aluno contemplar o belo e descobrir a harmonia existente nestas figuras sem deixar de formalizar o seu conhecimento.
The present work aims at using Fractal Geometry as a motivator in teaching areas and perimeters of Euclidean geometric figures. In addition, in order to contribute to a more pleasant and dynamic teaching of Mathematics combined with the use of technologies, it is proposed, through the Software Geogebra, the creation of activities to be developed in the context of the High School classroom in the development of mathematical concepts such as Geometric Progression, Geometry, Trigonometry, Logarithm and notions of limits, among other topics. The classic fractals are presented: Cantor's Carpet, Sierpinski's Carpet, Koch Island, Menger's Sponge, Dürer's Hexagonal Fractal, Dürer's Octagonal Fractal and the circular fractals: Circumtext Fractal, Tetracircle Fractal, Circular Antenna Fractal, Sieve Fractal Fractal Apollonius and Fractal Flower of Life. It is concluded that Fractal Geometry allows the students to contemplate the beauty and discover the harmony existing in these figures, without ceasing to formalize their knowledge.
The present work aims at using Fractal Geometry as a motivator in teaching areas and perimeters of Euclidean geometric figures. In addition, in order to contribute to a more pleasant and dynamic teaching of Mathematics combined with the use of technologies, it is proposed, through the Software Geogebra, the creation of activities to be developed in the context of the High School classroom in the development of mathematical concepts such as Geometric Progression, Geometry, Trigonometry, Logarithm and notions of limits, among other topics. The classic fractals are presented: Cantor's Carpet, Sierpinski's Carpet, Koch Island, Menger's Sponge, Dürer's Hexagonal Fractal, Dürer's Octagonal Fractal and the circular fractals: Circumtext Fractal, Tetracircle Fractal, Circular Antenna Fractal, Sieve Fractal Fractal Apollonius and Fractal Flower of Life. It is concluded that Fractal Geometry allows the students to contemplate the beauty and discover the harmony existing in these figures, without ceasing to formalize their knowledge.
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Fractais, Ensino médio, Geogebra, Fractal, High school