line at infinity sentence in Hindi
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- In projective geometry, a homothetic transformation is a similarity transformation ( i . e ., fixes a given elliptic involution ) that leaves the line at infinity pointwise invariant.
- The whole family of circles can be considered as " conics passing through two given points on the line at infinity " at the cost of requiring complex coordinates.
- The fundamental property that singles out all projective geometries is the " elliptic " group of transformations can move any line to the " line at infinity " ).
- This is true of the line at infinity itself; it meets itself at its two endpoints ( which are therefore not actually endpoints at all ) and so it is actually cyclical.
- On the other hand, starting with the real projective plane, a Euclidean plane is obtained by distinguishing some line as the line at infinity and removing it and all its points.
- In the real projective plane, since parallel lines meet at a point on the line at infinity, the parallel line case of the Euclidean plane can be viewed as intersecting lines.
- Since an ellipse does not intersect the line at infinity, it properly belongs to the affine plane determined by removing the line at infinity and all of its points from the projective plane.
- Since an ellipse does not intersect the line at infinity, it properly belongs to the affine plane determined by removing the line at infinity and all of its points from the projective plane.
- Assuming a given direction for the axis of the parabola implicitly provides two of these points, because the direction of the axis determines where the parabola is tangent to the line at infinity.
- In geometry and topology, the "'line at infinity "'is a projective line that is added to the real ( affine ) incidence properties of the resulting projective plane.
- The empty set may be the line at infinity considered as a double line, a ( real ) point is the intersection of two complex conjugate lines and the other cases as previously mentioned.
- Hyperbolas intersect the line at infinity in two distinct points and the polar lines of these points are the asymptotes of the hyperbola and are the tangent lines to the hyperbola at these points of infinity.
- Just as the Riemann sphere needs a north pole point at infinity to close up the complex projective line, so a line at infinity succeeds in closing up the plane of dual numbers to a cylinder.
- In the case of a parabola, that is, when, there is no center since the above denominators become zero ( or, interpreted projectively, the center is on the line at infinity .)
- The Euclidean plane is embedded in the real projective plane by adjoining a line at infinity ( and its corresponding points at infinity ) so that all the lines of a parallel class meet on this line.
- Historically there was a process by which projective geometry added more points ( " e . g . " complex points, line at infinity ) to simplify the geometry by refining the basic objects.
- To obtain the extended Euclidean plane, the absolute line is chosen to be the line at infinity of the Euclidean plane and the absolute points are two special points on that line called the circular points at infinity.
- Somewhat less intuitively, over the complex numbers, an ellipse intersects the line at infinity in a " pair " of points while a parabola intersects the line at infinity in a " single " point.
- Somewhat less intuitively, over the complex numbers, an ellipse intersects the line at infinity in a " pair " of points while a parabola intersects the line at infinity in a " single " point.
- However, if one were to consider the line at infinity as the directrix, then by taking the eccentricity to be a circle will have the focus-directrix property, but it is still not defined by that property.
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