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In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.
Non-Euclidean geometry, literally any geometry that is not the same as Euclidean geometry. Although the term is frequently used to refer only to hyperbolic geometry, common usage includes those few geometries (hyperbolic and spherical) that differ from but are very close to Euclidean geometry.
The history of non-Euclidean geometry is a fascinating subject, which is described very well in the introductory chapter of Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity by Steven Weinberg.
Non-Euclidian geometry is geometry done in spaces where Euclid's original rules (which are for flat planes) aren't true. Edit: this might sound extremely abstract but, thanks to a branch of physics called general relativity, we now understand that space (and time) can actually be curved.
Non-Euclidean space. A space whose properties are based on a system of axioms other than the Euclidean system. The geometries of non-Euclidean spaces are the non-Euclidean geometries.
If you decide not to assume Euclid’s Fifth, then… well, you get non-Euclidean geometry. One example of this is spherical geometry—the entire navigation theory is based on this. Another example is hyperbolic geometry. When Einstein was studying the structure of our universe, he needed non-Euclidean geometry.
10. Introduction to Non-Euclidean Spaces. MIT 8.286 The Early Universe, Fall 2013 View the complete course: http://ocw.mit.edu/8-286F13 Instructor: Alan Guth In this lecture, the professor ...
Non-Euclidean Geometry. In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the parallel postulate.
Understanding non-Euclidean geometry, a crucial foundation for Einstein's theory of general relativity and its exploration of curved space concepts.
Non-euclidean space plays a crucial role in modern physics, especially in Einstein's theory of general relativity. In this framework, spacetime is modeled as a curved structure rather than a flat one, which allows for the incorporation of gravity's effects on time and space.