plane

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plane1 / plān/ • n. 1. a flat surface on which a straight line joining any two points on it would wholly lie: the horizontal plane. ∎  an imaginary flat surface through or joining material objects: the planets orbit the sun in roughly the same plane. ∎  a flat or level surface of a material object: the plane of his forehead. ∎  a flat surface producing lift by the action of air or water over and under it. 2. a level of existence, thought, or development: everything is connected on the spiritual plane. • adj. completely level or flat. ∎  of or relating to only two-dimensional surfaces or magnitudes: plane and solid geometry. • v. [intr.] (of a bird or an airborne object) soar without moving the wings; glide: a bird planed down toward the water below. ∎  [intr.] (of a boat, surfboard, etc.) skim over the surface of water as a result of lift produced hydrodynamically. plane2 • n. an airplane. • v. [intr.] rare travel in an airplane. plane3 • n. a tool consisting of a block with a projecting steel blade, used to smooth a wooden or other surface by paring shavings from it. • v. [tr.] smooth (wood or other material) with a plane. ∎  [tr.] reduce or remove (redundant material) with a plane: high areas can be planed down. ∎ archaic make smooth or level.

plane

plane4 (also plane tree) • n. a tall spreading tree (genus Platanus, family Platanaceae) of the northern hemisphere, with maplelike leaves and bark that peels in uneven patches. See also sycamore.

Plane

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Plane

The term plane, together with point, line, and solid, is considered an undefined term. Every definition in mathematics attempts to use simpler and better-understood terms to define more complex ones. As the terms to be defined become ever simpler, this eventually becomes impossible. The simplest terms are so well understood that there is little sense in attempting a formal definition, since often the term itself must be used in the definition. The definition attributed to Euclid, in fact, relies on an intuitive understanding of the terms point, line, straight, and surface.

A plane is infinite in extent, both in length and width, so that flat physical objects are represented mathematically by some portion of a plane. A plane has only width and length. It has no thickness. While a plane is strictly two dimensional, so is the curved surface of a solid such as a sphere. In order to distinguish between curved surfaces and planes, Euclid devised a definition for plane similar to the following: given two points on a surface, the surface is planar if every point on the straight line that connects these two points is also on the surface.

Plane is a term used in mathematics (especially geometry) to express, in abstract form, the physical property of flatness. A point or line can be contained in a plane, a solid cannot. Instead, the intersection of a plane with a solid is a cross section of the solid consisting of a portion of the plane.

See also Locus.

Plane

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Plane

Generally, the term plane, together with point , line, and solid, is considered an undefined term. Every definition in mathematics attempts to use simpler and better understood terms to define more complex ones. As the terms to be defined become ever simpler, this eventually becomes impossible. The simplest terms are so well understood that there is little sense in attempting a formal definition, since often times the term itself must be used in the definition. Notice that the definition attributed to Euclid relies on an intuitive understanding of the terms point, line, straight, and surface. A plane is infinite in extent, both in length and width, so that flat physical objects are represented mathematically by some portion of a plane. A plane has only width and length. It has no thickness. While a plane is strictly two dimensional, so is the curved surface of a solid such as a sphere . In order to distinguish between curved surfaces and planes, Euclid devised a definition for plane similar to the following: given two points on a surface, the surface is planar if every point on the straight line that connects these two points is also on the surface. Plane is a term used in mathematics (especially geometry ) to express, in abstract form, the physical property of flatness. A point or line can be contained in a plane, a solid cannot. Instead, the intersection of a plane with a solid is a cross section of the solid consisting of a portion of the plane.

See also Locus.

plane

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plane In mathematics, a flat surface such that a straight line joining any two points on it lies entirely within the surface. Its equation in the three-dimensional Cartesian coordinates is ax + by + cz = d, where a, b, c, and d are constants.

plane

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plane (playn) n. a level or smooth surface, especially any of the hypothetical flat surfaces used to divide the body (see coronal, sagittal).

plane

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plane2 tool for smoothing surfaces. XIV. — (O)F., var. (under the infl. of vb. planer) of †plaine :- late L. plāna planing instrument, f. plānāre PLANE5.

plane

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plane5 †make level or even; smooth with a plane XIV (also pleyne, plaine, plain until XVIII). — (O)F. planer :— L. plānāre, f. plānus PLAIN.

plane

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plane3 plane surface. XVII. — L. plānum flat surface, sb. use of n. of plānus PLAIN.

plane

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plane4 level, flat. XVII. refash. of PLAIN adj. after F. plan, fem. plane.

plane

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plane1 tree of the genus Platanus. XIV. — (O)F.:— L. platanus — Gr. plátanos, f. stem of platús broad.

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plane (mathematics)

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