Geometrias não-euclidianas: história e aplicações

Abstract

This paper presents a brief study of non-Euclidean geometries: hyperbolic geometry and elliptical geometry. These geometries emerged from the attempts to demonstrate the postulated of Euclid's parallels as a proposition. We saw that the creation allowed the beginning of a vast field of knowledge and reasoning encompassing not only mathematics, but several sciences that benefited from new discoveries. We also present models of representation of these geometries in order to clarify their significant impact. Thus, we seek to show where real applications of these new knowledge are found, through several examples. Mathematicians, like all other scientists, are always in a state of research and understanding of the world and the universe in general, we have seen that this attitude can lead to amazingly amazing and useful results for mankind. Thus, at the end of this work, we try to reinforce the interest of studying and further deepening the mathematical knowledge, especially the geometry, considering the range of results obtained both for mathematics and for other sciences.