Semelhança, uma visão analítica

Abstract

The team paper revisits the teory about Similarity shown in the work Medida e Forma em Geometria, of Elon Lages Lima, searching for give it a comprehension more analytical. Afeter some definitions and preliminary concepts, the text includes a brief historical review of the changing notion of similarity over the years by making considerations about some works as: The Elements, of Euclides (about 300 a. C.), Élements de Géométrie, of Adrien-Marie Legendre (1794) and Léçons de Géométrie Élémentaire, of Jacques Salomon Hadamard (1898). Next, a way to characterize Similarity application is discussed as a composition of an specific homothety and isometry. Based on this caracterization, many properties about Similarity that Lima presents are demonstrated again under another theorical framework and, after, expended beyond euclidian plane and space. As a matter of fact, some aspects of similarity in Rn (in usual metric) and the similarity between figures that belong to different metric spaces, especially between a figure of euclidean plane and a figure of spherical plane, are treated.