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.

### Look at other dictionaries:

• 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

• Circle — This article is about the shape and mathematical concept. For other uses, see Circle (disambiguation). Circle illustration showing a radius, a diameter, the centre and the circumference …   Wikipedia

• infinity — /in fin i tee/, n., pl. infinities. 1. the quality or state of being infinite. 2. something that is infinite. 3. infinite space, time, or quantity. 4. an infinite extent, amount, or number. 5. an indefinitely great amount or number. 6. Math. a.… …   Universalium