Circle at infinity
Infinity In*fin"i*ty, n.; pl. {Infinities}. [L. infinitas; pref. in- not + finis boundary, limit, end: cf. F. infinit['e]. See {Finite}.] [1913 Webster] 1. Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity. --Sir T. More. [1913 Webster]

There can not be more infinities than one; for one of them would limit the other. --Sir W. Raleigh. [1913 Webster]

2. Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections. --Hooker. [1913 Webster]

3. Endless or indefinite number; great multitude; as an infinity of beauties. --Broome. [1913 Webster]

4. (Math.) A quantity greater than any assignable quantity of the same kind. [1913 Webster]

Note: Mathematically considered, infinity is always a limit of a variable quantity, resulting from a particular supposition made upon the varying element which enters it. --Davies & Peck (Math. Dict.). [1913 Webster]

5. (Geom.) That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity. [1913 Webster]

{Circle at infinity}, an imaginary circle at infinity, through which, in geometry of three dimensions, every sphere is imagined to pass.

{Circular points at infinity}. See under {Circular}. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

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• Line at infinity — Ideal line redirects here. For the ideal line in racing, see Racing line. In geometry and topology, the line at infinity is a line which is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the… …   Wikipedia

• Point at infinity — The point at infinity, also called ideal point, is a point which when added to the real number line yields a closed curve called the real projective line, mathbb{R}P^1. The real projective line is not equivalent to the extended real number line,… …   Wikipedia

• Plane at infinity — Plane Plane, n. [F. plane, L. plana. See {Plane}, v. & a.] 1. (Geom.) A surface, real or imaginary, in which, if any two points are taken, the straight line which joins them lies wholly in that surface; or a surface, any section of which by a… …   The Collaborative International Dictionary of English

• Circular points at infinity — Infinity In*fin i*ty, n.; pl. {Infinities}. [L. infinitas; pref. in not + finis boundary, limit, end: cf. F. infinit[ e]. See {Finite}.] [1913 Webster] 1. Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity. Sir T.… …   The Collaborative International Dictionary of English

• Circular points at infinity — Circular Cir cu*lar, a. [L. circularis, fr. circulus circle: cf. F. circulaire. See {Circle}.] [1913 Webster] 1. In the form of, or bounded by, a circle; round. [1913 Webster] 2. repeating itself; ending in itself; reverting to the point of… …   The Collaborative International Dictionary of English

• Circular points at infinity — In projective geometry, the circular points at infinity in the complex projective plane (also called cyclic points or isotropic points) are (1: i: 0) and (1: −i: 0). Here the coordinates are homogeneous coordinates (x: y: z); so that the line at… …   Wikipedia

• Infinity — In*fin i*ty, n.; pl. {Infinities}. [L. infinitas; pref. in not + finis boundary, limit, end: cf. F. infinit[ e]. See {Finite}.] [1913 Webster] 1. Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity. Sir T. More. [1913 …   The Collaborative International Dictionary of English

• Circle of confusion — For the closely related topic in microscopy, see Point spread function. In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as… …   Wikipedia