# 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 It might be outdated or ideologically biased.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 ?
Spontaneous passage rates were calculated as 70.8% in cases where the stone size on the axial plane was the same as or greater than on the the coronal plane; 56.2% in those where the coronal size was 1 mm greater than the axial size, and 34.7 in those where the coronal size was 2 mm or more than 2 mm greater than the axial size.
(b), (c) Local enlarged subtraction images of the left upper lung nodule with six successive slices in the axial and coronal planes. Clear enhanced shadows are seen in the subtraction images.
3-B.Lumbar range of motion in the coronal plane: The lumbar range of motion in the coronal plane was significantly lower under HC than under WOC conditions, both from the top of the swing to impact and from impact to finish (Table 1, bottom panel).
A pilot study on living subjects sought to determine the accuracy with which the Skeletal ML could be predicted using noninvasive measurements typically recorded by prosthetists during their everyday clinical practice, including sex, stature, anterior-posterior dimension (i.e., distance between the adductor longus tendon near its origin and the ischial tuberosity in sitting), and iliofemoral angle (i.e., soft tissue angle in the coronal plane between the lateral femoral shaft and gluteus medius in standing) [4].
Loading of the un-implanted tibial nail revealed negligible (< 0.25[degrees]; range: 0.10[degrees] to 0.23[degrees]) angular deflections in sagittal or coronal planes. Pure translation without angular deflection of the nail within the distal tibial construct was not observed in either the parallel or perpendicular screw orientation groups.
In both T1W & T2W MRI in axial, sagittal, coronal planes were evaluated.
Prosthetists generally evaluate sensations of static and dynamic balance in the sagittal and coronal planes, but there is no definitive or quantifiable method to obtain this essential information.
Duplication may occur in the sagittal (more common) or coronal planes, with the corresponding ipsilateral ureter draining each half of the urinary bladder.
Computed tomography (CT) in both axial and coronal planes identified an expansile soft-tissue-density mass that was confined to the left sphenoid and ethmoid sinuses with foci of calcification that had displaced the globe anterolaterally secondary to the extension of the mass through the medial wall of the orbit (figure 1).
All patients were studied in sagittal and coronal planes with multi-slice; spin-echo (T1 weighted acquisition) and fast scan (T2-weighted images) techniques.
This study extends work done in an earlier study [6] that focused on postures limited to the sagittal plane by testing the model for a range of postures in both the sagittal and coronal planes.

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