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 like surface is a straight line; a surface without curvature. [1913 Webster]

2. (Astron.) An ideal surface, conceived as coinciding with, or containing, some designated astronomical line, circle, or other curve; as, the plane of an orbit; the plane of the ecliptic, or of the equator. [1913 Webster]

3. (Mech.) A block or plate having a perfectly flat surface, used as a standard of flatness; a surface plate. [1913 Webster]

4. (Joinery) A tool for smoothing boards or other surfaces of wood, for forming moldings, etc. It consists of a smooth-soled stock, usually of wood, from the under side or face of which projects slightly the steel cutting edge of a chisel, called the iron, which inclines backward, with an apperture in front for the escape of shavings; as, the jack plane; the smoothing plane; the molding plane, etc. [1913 Webster]

{Objective plane} (Surv.), the horizontal plane upon which the object which is to be delineated, or whose place is to be determined, is supposed to stand.

{Perspective plane}. See {Perspective}.

{Plane at infinity} (Geom.), a plane in which points infinitely distant are conceived as situated.

{Plane iron}, the cutting chisel of a joiner's plane.

{Plane of polarization}. (Opt.) See {Polarization}.

{Plane of projection}. (a) The plane on which the projection is made, corresponding to the perspective plane in perspective; -- called also principal plane. (b) (Descriptive Geom.) One of the planes to which points are referred for the purpose of determining their relative position in space.

{Plane of refraction} or {Plane of reflection} (Opt.), the plane in which lie both the incident ray and the refracted or reflected ray. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

### Look at other dictionaries:

• Plane at infinity — In projective geometry, the plane at infinity is a projective plane which is added to the affine 3 space in order to give it closure of incidence properties. The result of the addition is the projective 3 space, P^3 . If the affine 3 space is… …   Wikipedia

• plane at infinity — Etymology: plane (IV) : the aggregate of all points at infinity in projective geometry of three dimensions …   Useful english dictionary

• 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

• Hyperplane at infinity — In mathematics, in particular projective geometry, the hyperplane at infinity, also called the ideal hyperplane, is an ( n −1) dimensional projective space added to an n dimensional affine space A, such as the real affine n space mathbb{R}^n , in …   Wikipedia

• 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.… …   The Collaborative International Dictionary of English

• point at infinity — an ideal mathematical point in projective geometry that preserves the magnitudes of all angles of a transformed plane …   Useful english dictionary

• 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 — 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

• 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