masterThesis
A história do surgimento da geometria não euclidiana: o despertar para novos mundos e os modelos de Beltrami
Fecha
2019-05-06Registro en:
SCHENA, Fernanda Mocelin. A história do surgimento da geometria não euclidiana: o despertar para novos mundos e os modelos de Beltrami. 2019. 100 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Tecnológica Federal do Paraná, Curitiba, 2019.
Autor
Schena, Fernanda Mocelin
Resumen
The present work presents a brief historical presentation of the development of the non-Euclidian models proposed by Eugenio Beltrami. From the precise systematization of Euclid, we present certain inquiries and misgivings about the local validity and global validity of the postulate of the parallels, including some misguided attempts at its demonstration over more than 2000 years, such as the work of Saccheri, and Gauss’s worries expressed in letters, to the contributions of János Bolyai. Finally, we highlight the role of Beltrami with the publication of his articles Saggio e Teoria, presenting metrics referring to spaces of constant and negative curvature. Some concepts of differential geometry are discussed, especially the models of the hyperboloid, Beltrami-Klein disc model, Riemann-Beltrami-Poincaré disk (conformal) and Liouville-Beltrami (conformal) semiplane model.