A geometria do disco de Poincaré
In this work, we discuss the history of non-Euclidean geometries, emphasizing a model of hyperbolic geometry in the plane: the Poincaré disk. We relate some results in this geometry to results from Euclidean geometry, such as the sum of the internal angles of a triangle, the area of a triangle, the...
| Autor principal: | Albon, Alfred James Dias |
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| Formato: | Trabalho de Conclusão de Curso (Graduação) |
| Idioma: | Português |
| Publicado em: |
Universidade Tecnológica Federal do Paraná
2022
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| Assuntos: | |
| Acesso em linha: |
http://repositorio.utfpr.edu.br/jspui/handle/1/29010 |
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| Resumo: |
In this work, we discuss the history of non-Euclidean geometries, emphasizing a model of hyperbolic geometry in the plane: the Poincaré disk. We relate some results in this geometry to results from Euclidean geometry, such as the sum of the internal angles of a triangle, the area of a triangle, the Pythagorean theorem and the laws of sines and cosines. We also use a dynamic geometry software, GeoGebra, to build tessellations on the Poincaré disk. We conclude that GeoGebra is an efficient tool to approach hyperbolic geometries in the plane. |
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