elliptic geometry wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org › wiki › Elliptic_geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than
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See moreIn elliptic geometry, two lines perpendicular to a given line must intersect. In fact, the perpendiculars on one side all intersect at a single point called the absolute pole of that line. The perpendiculars on the
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See moreNote: This section uses the term "elliptic space" to refer specifically to 3-dimensional elliptic geometry. This is in contrast to the previous section, which was about 2-dimensional
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See moreBecause spherical elliptic geometry can be modeled as, for example, a spherical subspace of a Euclidean space, it follows that if Euclidean geometry
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See moreElliptic plane
The elliptic plane is the real projective plane provided with a metric: Kepler and Desargues used the gnomonic projection to relate a plane σ to points on a hemisphere tangent to it. With O the center of the hemisphere, a point P in σ...
See moreHyperspherical model
The hyperspherical model is the generalization of the spherical model to higher dimensions. The points of n-dimensional elliptic space...
See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org › wiki › Talk:Elliptic_geometry
Elliptic geometry is the one where the poles in spherical geometry are identified. These are the only two globally isotropic spaces of constant positive curvature but there are other compact topologies which are locally isotropic. This distinction is relevant for cosmological world models and FAIK the terminology is not very standard.
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- https://en.wikipedia.org › wiki › Ellipse
In analytic geometry, the ellipse is defined as a quadric: the set of points (,) of the Cartesian plane that, in non-degenerate cases, satisfy the implicit equation + + + + + = provided <. To distinguish the degenerate cases from the non-degenerate case, let ∆ be the determinant = [] = +. Then the ellipse is a non-degenerate real ellipse if and only if C∆ < 0. If C∆ > 0, we have an ...
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- https://en.wikipedia.org › wiki › Elliptic_curve
Although the formal definition of an elliptic curve requires some background in algebraic geometry, it is possible to describe some features of elliptic curves over the real numbers using only introductory algebra and geometry.
In this context, an elliptic curve is a plane curve defined by an equation of the form
after a linear change of variables (a and b are real numbers). This type of equation is called a We…Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 7 mins
- https://encyclopediaofmath.org › wiki › Elliptic_geometry
Thus, elliptic geometry is the geometry of real projective space endowed with positive sectional curvature (i.e. the geometry of the sphere in $ \mathbf R ^ {n} $ with antipodal points, or antipodes, identified). An exposition of it is given in [a1], Chapt. 19; generalizations are given in [a2]. Some details follow.
Elliptic geometry - HandWiki
https://handwiki.org › wiki › Elliptic_geometryShort description: Non-Euclidean geometry . Geometry; Projecting a sphere to a plane.
- https://en.wikipedia.org › wiki › Non-Euclidean_geometry
Background. 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 legitimate until the 19th century.. The debate that eventually led to the discovery of the non-Euclidean geometries began almost as soon as Euclid wrote Elements.In the Elements, Euclid …
