Uma revolução científica na matemática : do paradigma pitagórico ao paradigma euclidiano

Abstract

This dissertation has as study object the analysis of the constitution of the incommensurable measures - or irrational numbers - for the theory of the science elaborated for Thomas Kuhn. The problem if delimits in the understanding of the constitution of the paradigm pythagorean and the euclidean paradigm. The main objective of this work was to identify if the discovery of the incommensurable measures caused rupture in the development of mathematical science, identifying in the historical elaboration of this theory a discontinuity in the process of construction of the mathematical knowledge. The adopted methodological procedure was bibliographical the documentary research and for survey and analysis of the historical texts. As result, we got that the kunhniana theory can be applied in its aspects central offices to the historical and epistemological study of the mathematics, in specific, the change of the pythagorean mathematics for euclidean geometry.