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 ?
The essays consider non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), but also de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski, Hermitian geometries, and others.
In the past, he has referred to the knitted works he makes as "portals." And indeed, at Marc Selwyn Fine Art, these fabrications were distinctly revealing of the artist's process and the ideas currently driving him, namely quantum physics and non-Euclidean geometry. In the tangram-esque Index-Manifold, 2017, for instance, Hansen fit together sixteen triangular, stretched-knit panels to form a rectangle.
He found himself able to elaborate a perfect system of non-Euclidean Geometry without doing violence to any other axiom or reaching any contradictory internally inconsistent results.
Non-Euclidean geometry was included to show a different perspective and geometrical sense than the one we live in.
Finally, he concluded by solving in non-Euclidean geometry one of the classical problems of geometry: SQUARING TF1E CIRCLE [capitalization added for emphasis] i.e., constructing a square equal in area to a given circle.
Mariconda's perceptive analysis of the author's rhetorical use of menacing sound, asymmetry, and non-Euclidean geometry is of particular importance to contemporary art and media theory.
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.