Non-Euclidean geometries

Authors

  • José Rubén Morones Ibarra Universidad Autónoma de Nuevo León

DOI:

https://doi.org/10.29105/ingenierias26.94-792

Keywords:

Non-euclidian geometries, Euclide's fifth postulate, hyperbolic geometry, Riemannian geometry

Abstract

Euclidean geometry is founded on five postulates that are presented as self-evident truths, which cannot be doubted. For a long time it was thought that there could be no geometry other than Euclid's. However, doubts about the independence of the fifth postulate with respect to the other four, opened the way for the development of new geometries. The philosophical impact of non-Euclidean geometries caused a revolution in mathematical thought, transforming mathematics into an even more abstract science and opening the possibility of conceiving more complex spaces. The development of the theory of relativity, for example, would not have been possible without the antecedent of non-Euclidean geometries. At the present time the applications of non-Euclidean geometries cover many fields of human endeavor, such as science, mechanical engineering, construction, architecture, art and in the mathematic itself.

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Author Biography

José Rubén Morones Ibarra, Universidad Autónoma de Nuevo León

He has a degree in Physical-Mathematical Sciences from the Universidad Autónoma de Nuevo León. He obtained a PhD in Physics in the area of ​​Theoretical Nuclear Physics, from the University of South Carolina, USA. He is currently a full-time research professor at the Facultad de Ciencias Físico Matemáticas, UANL He belongs to the National System of Researchers with Level I and is a Regular Member of the Mexican Academy of Sciences.

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Published

2023-01-30

How to Cite

Morones Ibarra, J. R. (2023). Non-Euclidean geometries. Revista Ingenierías, 26(94), 42–58. https://doi.org/10.29105/ingenierias26.94-792

Issue

Vol. 26 No. 94 (2023): Enero-Junio 2023

Section

Artículos

License

Copyright (c) 2023 José Rubén Morones Ibarra

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This work is licensed under a Creative Commons Attribution 4.0 International License.