non-Euclidean geometry


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Related to non-Euclidean geometry: hyperbolic geometry

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 ?
To conclude, he introduces non-Euclidean geometry and curvature, and explains why it is called hyperbolic.
In week 11, along with non-Euclidean geometry the interactions of mathematics with art, literature, science and philosophy were addressed via the symmetry and mathematical theory used in the drawings of the Dutch artist M.
Finally, he concluded by solving in non-Euclidean geometry one of the classical problems of geometry: SQUARING TF1E CIRCLE [capitalization added for emphasis] i.
To understand its defining characteristics in greater depth we study them in Euclidean geometry and in a particular non-Euclidean geometry system known as 'taxicab geometry'.
New York designer Jill Malek's Voyageur wallpaper takes non-Euclidean geometry to the next level, with a range of papers printed with lines radiating from points, like a compass gone wild.
If we set out to solve a problem by non-euclidean geometry, we don't switch to euclidean postulates.
In non-Euclidean geometry the ratio of a circle's circumference to its diameter may also differ from [pi].
The topics are non-Euclidean geometry, crossroads between hyperbolic geometry and number theory; origamis in TeichmA1/4ller space; 3-manifold topology; globally symmetric spaces; the geometry of the representation spaces in SU(2); the algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs; and asymptotic geometry.
It is also known as a type of non-Euclidean Geometry, being in many respects similar to Euclidean Geometry.
A Simple Non-Euclidean Geometry and its Physical Basis, Springer, New York--Heidelberg--Berlin, 1979.
Ivan Karamazov sees his inability to grasp non-Euclidean geometry as evidence that he can't understand God.