On Euclidean diagrams and geometrical knowledge

Autor(es)

Dal Magro, Tamires ^[1] ; Garcia-Perez, Manuel J. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Campinas, SP - Brazil

^[2] Univ Seville, Seville - Spain

• Tipo de documento: Artigo Científico
• Fonte: THEORIA-REVISTA DE TEORIA HISTORIA Y FUNDAMENTOS DE LA CIENCIA; v. 34, n. 2, p. 255-276, MAY 2019.
• Citações Web of Science: 0

Resumo

We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert's formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based practice strictly regimented, it is rooted in cognitive abilities that are universally shared. (AU)

• Processo FAPESP: 16/20480-5 - A epistemologia dos diagramas euclidianos
• Beneficiário: Tamires Dal Magro
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 14/23191-9 - Raciocínio formal e diagramático nas provas Euclidianas por redução ao absurdo
• Beneficiário: Tamires Dal Magro
• Modalidade de apoio: Bolsas no Brasil - Doutorado