Conceptualization and Acceptance of Non-Euclidean Geometries

Geometry is made up of theorems and propositions that are based on postulates induced by experience. Until the 18th century, the fundamental postulates of Greek geometry were five. However, the fifth postulate became the most studied and discussed. The objective is to demonstrate that the great debates were fruitful and that the impossibility of proving the fifth postulate led to the creation of other consistent and possible geometries. The systemic and analytical method that we use allows us to see the real applications of non-Euclidean geometries, atomic nuclei, speed of sea waves, catenary, air routes, notable elements and others. Finally, relativistic theories about the configuration of space and time lead to the conclusion, the great challenge of determining whether real physical space is a Euclidean space.