non-euclidean geometry wikipedia - EAS
- Non-Euclidean geometry is a type of geometry. Non-Euclidean geometry only uses some of the " postulates " ( assumptions) that Euclidean geometry is based on. In normal geometry, parallel lines can never meet. In non-Euclidean geometry they can meet, either infinitely many times ( elliptic geometry ), or never ( hyperbolic geometry ).
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See all on Wikipediahttps://en.wikipedia.org/wiki/Non-Euclidean_geometryIn 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
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See moreBackground
Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, and geometries that deviated from this were not widely accepted as...
See moreTwo dimensional Euclidean geometry is modelled by our notion of a "flat plane".
Elliptic geometry
The simplest model for elliptic geometry is a sphere, where lines are "great circles" (such as the equator or the meridians on a globe),...
See moreBefore the models of a non-Euclidean plane were presented by Beltrami, Klein, and Poincaré, Euclidean geometry stood unchallenged as the
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See moreHyperbolic geometry found an application in kinematics with the physical cosmology introduced by Hermann Minkowski in 1908. Minkowski introduced
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See moreEuclidean geometry can be axiomatically described in several ways. Unfortunately, Euclid's original system of five postulates (axioms) is not one of these, as his proofs relied on several unstated assumptions that should also have been taken as axioms.
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See moreEuclidean and non-Euclidean geometries naturally have many similar properties, namely those that do not depend upon the nature of parallelism. This
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See moreIn analytic geometry a plane is described with Cartesian coordinates : C = { (x,y) : x, y ∈ ℝ }. The points are sometimes identified with complex numbers z =
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See moreWikipedia text under CC-BY-SA license- https://simple.wikipedia.org/wiki/Non-Euclidean_geometry
In non-Euclidean geometry they can meet, either infinitely many times (elliptic geometry), or never (hyperbolic geometry). An example of Non-Euclidian geometry can be seen by drawing lines on a ball or other round object, straight lines that are parallel at the equator can meet at the poles Origin. It is called "Non-Euclidean" because it is different from Euclidean geometry, which was …
- https://en.wikipedia.org/wiki/Models_of_non-Euclidean_geometry
Models of non-Euclidean geometry are mathematical models of geometries which are non-Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l. In hyperbolic geometric models, by contrast, there are infinitely many lines through A parallel to l, and in elliptic geometric models, parallel lines do not exist. (See the entries on hyperbolic geometry and elliptic geometry for more information.)
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- https://en.wikipedia.org/wiki/Category:Non-Euclidean_geometry
The main article for this category is Non-Euclidean geometry. Within contemporary geometry there are many kinds of geometry that are quite different from Euclidean geometry, first encountered in the forms of elementary geometry, plane geometry of triangles and circles, and solid geometry. The conventional meaning of Non-Euclidean geometry is the one set in the …
- https://math.fandom.com/wiki/Non-Euclidean_geometry
- While Euclidean geometry, named after the Hellenistic Egyptian mathematician Euclid, includes some of the oldest known mathematics, non-Euclidean geometries were not widely accepted as legitimate in the Western world until the 19th century. The debate that eventually led to the discovery of non-Euclidean geometries began almost as soon as Euclid's ...
- https://en.wikipedia.org/wiki/Euclidean_geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these.Although many of Euclid's results had been stated earlier, Euclid was the first to organize …
- https://en.wikipedia.org/wiki/Talk:Non-Euclidean_geometry
There are a great many geometries which are not Euclidean geometry, but only these two are referred to as the non-Euclidean geometries. Some mathematics teachers may assert this claim, but generally it is not true. Galilean geometry and Minkowski geometry are non-Euclidean and widely addressed to support physical notions.
- https://en.wikipedia.org/wiki/Geometry
Later in the 19th century, it appeared that geometries without the parallel postulate ( non-Euclidean geometries) can be developed without introducing any contradiction. The geometry that underlies general relativity is a famous application of non-Euclidean geometry.
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