Construção de geometrias: uma abordagem axiomática

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Universidade Federal de Goiás


In basic education or in the teaching of geometry, it is shown that there are no reflexions and questions about the construction of geometry: How is geometry born? Or, how to build geometry from nothing? Inquiries about some fundamentals of geometry are fundamental to understanding how mathematics is built. However, it turns out to be a simple task to find ways of approach in basic education that provides these reflexions, since geometry returns to students and is exposed as an absolute truth. It is in this sense, that the present work approaches a process of geometry construction, through the insertion of axioms at a time and is analyzed as its consequences in this geometry. To do so, recover the notion of models in a geometry, which will be attributed to this construction, indicated by the teacher as a tool that can subsidize the reflexions and questions about the construction of plane geometry.



Axiomas, Geometrias, Modelos, Axioms, Geometry, Models


NASCIMENTO, D. L. Construção de geometrias: uma abordagem axiomática. 2020. 100 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2020.