Demonstration of Cauchy: Understanding Algebraic
DOI:
https://doi.org/10.36560/1120127Keywords:
History of Mathematics, Euler's Theorem on Polyhedra, Demonstration of CauchyAbstract
ABSTRACT: In this study we present some considerations about the End of Course Work undergraduate Full Degree in Mathematics / UFMT, drafted in 2011, and by taking title "A story about Cauchy and Euler's theorem on polyhedra" that gave birth to our research project Master of Education, begun in 2012, on the approaches of Euler's theorem on polyhedra in mathematics textbooks. At work in 2011 presented some considerations about the history of Euler's theorem for polyhedra which focus the demonstration presented by Cauchy (1789-1857), who tries to generalize it, relying on assumptions not observable in Euclidean geometry. Therefore, we seek the accessible literature on the history of mathematics; relate some aspects of the demonstration Cauchy with historical events on the development of mathematics in the nineteenth century, which allowed the acceptance of such a demonstration by mathematicians of his time.
Keywords: History of Mathematics. Euler's Theorem on Polyhedra. Demonstration of Cauchy.
References
BOYER, C.B.. História da Matemática. Revista por Uta C. Merzbach; tradução: Elza F. Gomide – 2° Ed.- São Paulo: Edgard Blüncher, 1996.
BLANCHÉ, R. A Axiomática. São Paulo/ Rio de Janeiro: Martins Fontes, 1978
COURANT, R.; ROBBINS, H.. O que é Matemática? Rio de Janeiro: Editora Moderna Ltda., 2000.
DIENES, Z.P. A geometria pelas transformações - I Topologia, Geometria Projetiva e Afim. Trad.: Maria P. B. M. Chalier e René F. J. Chalier, São Paulo, EPU. BrasÃlia, INL, 1975.
EVES, H.. História da Geometria. Trad. Hygino H. Domingues, (Tópicos de História da Matemática para uso em sala de aula; v. 3). São Paulo: Atual, 1992.
LIMA, E.L.. O Teorema de Euler sobre Poliedros. In: Meu Professor de Matemática e outras Histórias - Coleção do Professor de Matemática, SBM; IMPA, 1991.
MARTINES, M.C.S. Algumas observações sobre a caracterÃstica de Euler: Uma Introdução de Elementos da História da Matemática no Ensino Médio. Dissertação
de mestrado. UNESP, Rio Claro/ SP: 2009.
TOMEI, C.. Euclides - a conquista do espaço. Ilustrador Libero Malavoglia – São Paulo: Odysseus Editora — (Imortais da Ciência/ coordenação Marcelo Gleiser) ,
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