plane (redirected from planes)

plane, in mathematics, flat surface of infinite extent but no thickness. An example of a plane, or more exactly of a bounded portion of a plane, is the surface forming one face, or side, of a cube. A plane is determined, or defined, by any of the following: (1) three points not in a straight line; (2) a straight line and a point not on the line; (3) two intersecting lines; or (4) two parallel lines. Two straight lines in space do not usually lie in the same plane. For a given plane in space, a line can either lie outside and parallel to it, intersect the plane in a single point, or lie entirely in the plane; if more than one point of a straight line lies in the plane, then the entire line must lie in the plane.

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plane¹

1. Maths a flat surface in which a straight line joining any two of its points lies entirely on that surface

2. 

a. short for aeroplane

b. a wing or supporting surface of an aircraft or hydroplane

3. Maths (of a curve, figure, etc.) lying entirely in one plane

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plane²

1. a tool with an adjustable sharpened steel blade set obliquely in a wooden or iron body, for levelling or smoothing timber surfaces, cutting mouldings or grooves, etc.

2. a flat tool, usually metal, for smoothing the surface of clay or plaster in a mould