# 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.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.

## 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
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
"That's the first one, and from there on we have several other similar opportunities such as Frigg and Barnacle where we can work on both sides of the median line."
Turkmenistan says that Caspian is a confined environment, and fairness and commonsense demand that the median line be drawn right through the middle of the sea, equidistant at all points from the main shoreline.
(27) The Defense of Japan 2007 noted that by operating PLAN vessels near the median line, "China aimed to highlighting [sic] its Navy's capabilities to acquire, maintain and protect maritime rights and interests." (28)
Provided that, where any part of that line lies beyond the median line ("The median line" here is the line every point of which is equidistant from the nearest point on the baseline of Japan and the nearest point on the baseline from which the breadth of the territorial sea pertaining to the foreign coast which is opposite the coast of Japan is measured.
A white median line from apex of frons to end of mesonotum, along lateral carinae of frons, gena, and pronotum with white line; forewings with pale brown over basal third, rest area hyaline, along apical veins bordered brown stripes, in dark portion veins bear white spots; male with abdomen most blackish brown, female with abdomen most yellowish brown, ovipositor brown."
The Australian government maintains that in international law a median line is not required when two countries do not have a continental shelf in common.
The ICJ adopted a modified median line. Did equity provide any guidelines?
Taiwan's defense ministry on Tuesday (July 30) refuted reports that the military drill carried out by China on Monday took place across the median line of the Taiwan Strait.
Equinor is partnered with Shell on Lifjellet, the final prospect, which lies near the median line with Norway.
Not being a party to Unclos did not prevent Turkey from recognising customary international law, which states that the exclusive economic zone is understood to be the median line between the shores of two neighbouring countries.
It comes after Taiwan's Ministry of National Defence (MND) said earlier this month that two Chinese J-11 fighter jets crossed the Taiwan Strait's "median line" on 31 March, prompting Taipei to scramble several aircraft in order to intercept the warplanes.
"We agreed to immediately commence talks to conclude a bilateral Framework Agreement regarding the development of hydrocarbon reserves that extend beyond the median line between the EEZ of both countries," said Christodoulides.

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