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
ThesaurusAntonymsRelated WordsSynonymsLegend:
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 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.
Ivan Karamazov sees his inability to grasp non-Euclidean geometry as evidence that he can't understand God.
1040) on the foundations of Euclidean geometry, leading him in the process to prove theorems in non-Euclidean geometry, including a formulation of what is today called the Strong Hilbert Axiom of Parallels.
Parsons puts the point this way: "the development of non-Euclidean geometry and its applications in physics were, historically, the main reasons why Kant's theory of geometry and space came to be rejected.
The Fifth Postulate: How Unraveling a Two-Thousand-Year-Old Mystery Unraveled the Universe Jason Socrates Bardi The story of the discovery of non-Euclidean geometry.
Did people have some inkling of non-Euclidean geometry, some premonition that the parallel postulate might be false?