Geometria e aritmética: um encaixe imperfeito
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Data
2022-03-24
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Universidade Federal de Goiás
Resumo
In the present work we clarify how the discovery of incommensurable magnitudes
impacted Greek mathematics and how, even today, we experience the consequences of
this fact. Furthermore, contrasting Eudoxus' doctrine on ratio and proportion and
Descartes' formulations that enabled an arithmetical treatment of geometric quantities, we
show how, at the beginning of modernity, the effort to overcome the abyss between
Geometry and Arithmetic took shape. Finally, exploring the divergences between modern
mathematicians and contemporary constructivists regarding the notion of existence, we
show how, by adopting a more rigorous conception of existence as meaning “hand
possession” of a method for identifying mathematical objects, the imperfect fit between
Geometry and Arithmetic then returns to the fore, thus rehabilitating the distinction
between numbers and magnitudes and the logical independence between geometric
proofs and arithmetic proofs.
Descrição
Palavras-chave
Geometria, Aritmética, Incomensurabilidade, Existência, Geometry, Arithmetic, Incommensurability, Existence
Citação
RIBEIRO, André Luiz. Geometria e aritmética: um encaixe imperfeito. 2022. 45f. Trabalho de Conclusão de Curso (Graduação) – Unidade Acadêmica Especial de Ciências Humanas, Universidade Federal de Goiás, Cidade de Goiás, 2022.