plane

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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.

Plane

The simplest kind of two-dimensional surface, generated by the path of a straight line and defined by its length and width. The fundamental property of a plane is its shape and surface characteristics.

Plane

 

one of the fundamental concepts in geometry. In a systematic exposition of geometry, a plane is usually considered as an initial concept, which is only indirectly defined by the axioms of geometry. Its characteristic properties include the following: (1) A plane is a surface such that every line connecting any two of its points lies entirely within the surface. (2) A plane is a set of points equidistant from two given points.

REFERENCES

Efimov, N. V. Vysshaia geometriia, 5th ed. Moscow, 1971.
Hilbert, D. Osnovaniia geometrii. Moscow-Leningrad, 1948. (Translated from German.)

Plane

 

a wood-shaving tool consisting of a wooden or metal stock, a cutter, and a wedge. The earliest planes, discovered in Pompeii, date to the first century A.D. Little use was made of the plane in ancient times and in the Middle Ages, the principal planing tool being the drawknife; widespread use of the plane began in the 15th and 16th centuries.

There are several types of planes, classified according to the type of planing (flat or profile planing), the stock size, and the cutter profile and angle adjustment. Jack planes are used for rough, flat planing with a rounded cutting blade. Single- and double-iron planes with chip breakers and trying planes, which are elongated and have two handles, are used for finish planing. Jointer planes and long planes, the latter distinguished by extreme length of the stock, are used for finish planing, for planing large, flat areas using a straight edge to check for the finish desired, and for fitting parts. Especially thin layers of wood are removed with smoothing planes. Toothing planes are used for making fine grooves on the surfaces of parts to be glued. Rabbets can be cut with rabbet planes and trimmed with fillister planes. Matching planes are used for making grooves, and router planes cut trapeziform slots against the grain. Irregularly shaped patterns on the faces of parts are worked with molding planes. Compass planes have a curved stock and are used in working curved (concave or convex) surfaces. Electric-powered hand planes are also used.

plane

[plān]
(electronics)
Screen of magnetic cores; planes are combined to form stacks.
(design engineering)
A tool consisting of a smooth-soled stock from the face of which extends a wide-edged cutting blade for smoothing and shaping wood.
(mathematics)
A surface such that a straight line that joins any two of its points lies entirely in that surface.
In projective geometry, a triple of sets (P, L, I) where P denotes the set of points, L the set of lines, and I the incidence relation on points and lines, such that (1) P and L are disjoint sets, (2) the union of P and L is nonnull, and (3) I is a subset of P × L, the cartesian product of P and L.

plane

plane, 1
1. A tool for smoothing wood surfaces; consists of a smooth soleplate, from the under-side of which projects slightly the cutting edge of an inclined blade; there is an aperture in front of the blade for the shavings to escape.
2. A surface, any section through which by a like surface is a straight line.
3. Of a column, the surface of a longitudinal section through the axis of the column.

plane

1
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

plane

2
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
References in periodicals archive ?
In concrete terms, we will undertake joint development in the northern part of the East China Sea and on the Chinese side of the median line at Shirakaba, and Japanese corporations will participate in the development at the location where China has already undertaken development.
There is a clear understanding that since the distance between their shorelines is less than 400 nautical miles (about 740 km), the conventional limits of EEZ (Exclusive Economic Zone) cannot be applied, and therefore a median line should be drawn to mark the share of each side.
Recognizing that Chinese and Japanese claims would overlap and that delimitation negotiations would be lengthy, Japan adopted a median line with regard to the Chinese claim in its declaration.
Finally, as Ma reported, this measure failed to show sensitivity to the magnitude of intervention data points above the median line.
At Tuesday's talks, the South Korean side strongly demanded a median line on the boundaries of the two nations' zones be drawn between Dokdo, instead of Ullung Island, and Japan's Oki islands, Yonhap said.
Australian Department of Foreign Affairs and Trade: Australia's position remains that it has sovereign rights under international law to the natural resources on our continental shelf, in any event, Greater Sunrise lies almost entirely on the Australian side of the median line.
in Britain, has been preparing to develop the oil field which straddles the two countries' median line in cooperation with other companies, including Paladin Expro Ltd.
There is no rule to say you must have a median line if the two countries do not have a common continental shelf.
In short, the East Timorese argue that a seabed boundary should be based on a median line between the two countries, which would give East Timor exclusive access to the JDPA, and to a majority of the oil and gas fields.
Putin: "We agreed to begin work on drawing a median line between Russia and Azerbaijan".
Two apparently very large oil discoveries have been announced in the last few weeks: one, about which little is yet known, is in the Dutch waters in the southern part of the North Sea; the other, named Ekofisk, is in Norwegian waters, just over the median line from the British sector.