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- Q1191139 subject Q7164757.
- Q1191139 subject Q7413888.
- Q1191139 subject Q8824657.
- Q1191139 abstract "In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring.In the real case, a point at infinity completes a line into a topologically closed curve. In higher dimensions, all the points at infinity form a projective subspace of one dimension less than that of the whole projective space to which they belong. A point at infinity can also be added to the complex line (which may be thought of as the complex plane), thereby turning it into a closed surface known as the complex projective line, CP1, also called the Riemann sphere (when complex numbers are mapped to each point).In the case of a hyperbolic space, each line has two distinct ideal points. Here, the set of ideal points takes the form of a quadric.".
- Q1191139 thumbnail Real_projective_line.svg?width=300.
- Q1191139 wikiPageWikiLink Q1307734.
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- Q1191139 wikiPageWikiLink Q381892.
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- Q1191139 wikiPageWikiLink Q5958478.
- Q1191139 wikiPageWikiLink Q650741.
- Q1191139 wikiPageWikiLink Q7164757.
- Q1191139 wikiPageWikiLink Q7201011.
- Q1191139 wikiPageWikiLink Q7413888.
- Q1191139 wikiPageWikiLink Q7524253.
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- Q1191139 wikiPageWikiLink Q864919.
- Q1191139 wikiPageWikiLink Q877775.
- Q1191139 wikiPageWikiLink Q8824657.
- Q1191139 comment "In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added.".
- Q1191139 label "Point at infinity".
- Q1191139 depiction Real_projective_line.svg.