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TRILOGUE INfinity - translation to English
![The first three steps of a fractal construction whose limit is a [[space-filling curve]], showing that there are as many points in a one-dimensional line as in a two-dimensional square.](https://commons.wikimedia.org/wiki/Special:FilePath/Peanocurve.svg?width=200 "The first three steps of a fractal construction whose limit is a [[space-filling curve]], showing that there are as many points in a one-dimensional line as in a two-dimensional square.")
![By [[stereographic projection]], the complex plane can be "wrapped" onto a sphere, with the top point of the sphere corresponding to infinity. This is called the [[Riemann sphere]].](https://commons.wikimedia.org/wiki/Special:FilePath/Riemann sphere1.svg?width=200 "By [[stereographic projection]], the complex plane can be \"wrapped\" onto a sphere, with the top point of the sphere corresponding to infinity. This is called the [[Riemann sphere]].")
[in'finiti]
общая лексика
бесконечно удаленная точка
бесконечность
беспредельность
Смотрите также
существительное
общая лексика
бесконечность (также [мат.])
что-л. огромное
бесконечное
безграничное
бесконечно большое число
количество
бесконечность
безграничность
Definition
Wikipedia
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.
