Definitions for non-euclidean geometry
non-eu·clidean ge·om·e·t·ry

Princeton's WordNetRate this definition:0.0 / 0 votes

1. non-Euclidean geometrynoun

   (mathematics) geometry based on axioms different from Euclid's

   "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"

WiktionaryRate this definition:0.0 / 0 votes

1. non-Euclidean geometrynoun

   Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience.

WikipediaRate this definition:0.0 / 0 votes

1. Non-Euclidean geometry

   In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called non-Euclidean geometry. The essential difference between the metric geometries is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, while in elliptic geometry, any line through A intersects l.

ChatGPTRate this definition:0.0 / 0 votes

1. non-euclidean geometry

   Non-Euclidean geometry is a type of geometry that rejects the validity of Euclid's fifth postulate, also known as the parallel postulate, which states that through a point not on a given line, there is exactly one line parallel to the given line. In non-Euclidean geometry, either many or no lines exist that are parallel to the given line. This category of geometry includes hyperbolic geometry and elliptic geometry, which are fundamentally different from the flat geometry described by Euclid, known as Euclidean geometry. Non-Euclidean geometries are used in the theory of general relativity and in the modeling of certain types of spaces.

WikidataRate this definition:0.0 / 0 votes

1. Non-Euclidean geometry

   In mathematics, non-Euclidean geometry is a small set of geometries based on axioms closely related to those specifying Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is set aside. In the latter case one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras which give rise to kinematic geometries that have also been called non-Euclidean geometry. The essential difference between the metric geometries is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line ℓ and a point A, which is not on ℓ, there is exactly one line through A that does not intersect ℓ. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting ℓ, while in elliptic geometry, any line through A intersects ℓ.

Matched Categories

1. • Geometry
   • Mathematics

How to pronounce non-euclidean geometry?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say non-euclidean geometry in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of non-euclidean geometry in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of non-euclidean geometry in Pythagorean Numerology is: 9

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=non-euclidean geometry
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Non-Euclidean_Geometry
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Non-Euclidean_Geometry
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=non-euclidean geometry