non-Euclidean geometry

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non-Euclidean geometry

n
(Mathematics) the branch of modern geometry in which certain axioms of Euclidean geometry are restated. It introduces fundamental changes into the concept of space
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Noun1.non-Euclidean geometry - (mathematics) geometry based on axioms different from Euclid's; "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"
math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
geometry - the pure mathematics of points and lines and curves and surfaces
hyperbolic geometry - (mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane; "Karl Gauss pioneered hyperbolic geometry"
elliptic geometry, Riemannian geometry - (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle; "Bernhard Riemann pioneered elliptic geometry"
References in periodicals archive ?
Non-Euclidean geometries, Mobius band and Klein bottle were not in the original syllabus, but we have included them in the course content, because Klein bottle is a well-known 4D object and mentioned in the discussion on dimension.
This challenges theorists in the natural scientists to discover these recursive non-Euclidean geometries in nature.
4) To demolish Einstein's theories of relativity (in elliptic geometry), you could go back and prove the parallel postulate, bringing down not only Einstein, but all of the non-Euclidean geometries, as well.
While all students have generally been exposed to Euclidean geometry, most do not know much about non-Euclidean geometries and are very intrigued, if at times baffled, by this different perspective.
Kant's critical philosophy, perhaps the only serious rival to realism in the minds of some scientists, crashed and burned in the nineteenth century with the development of non-Euclidean geometries and their later incorporation into the non-Newtonian physics of relativity in the early twentieth century.
His "Explanations of the Difficulties in the Postulates of Euclid", which tackled the problems of parallels opened the floodgates of non-Euclidean geometries.
Know that variants of the Parallel Postulate produce non-Euclidean geometries (e.
And yet, non-Euclidean geometries do not require an experiential counterpart.