Definition:Linear Measure
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Definition
Linear measure is the means of measurement of physical displacement.
Dimension
Linear measure is one of the fundamental dimensions of physics.
In dimensional analysis it is assigned the symbol $L$ or $\mathbf L$.
Units
- The SI unit of linear measure is the meter $\mathrm m$.
- The CGS unit of linear measure is the centimeter $\mathrm {cm}$.
Thus:
- $1 \ \mathrm m = 10^2 \ \mathrm {cm} = 100 \ \mathrm {cm}$
Length
Length is distance measured in one direction. Usually, in multi-dimensional figures, the dimension in which the distance is longest is referred to as length.
It is the most widely used term for linear measure, as it is the standard term used when only one dimension is under consideration.
Breadth
Also known as width.
Breadth is distance measured in a second dimension, perpendicular to length and in the plane of the figure (in the case of a two-dimensional figure).
Also see height.
In a three-dimensional figure, the choice of which direction is referred to as width is often arbitrary.
Depth
Depth is distance measured in a third dimension, perpendicular to both length and breadth.
The choice of depth is often arbitrary, although in two-dimensional diagrams of three-dimensional figures, depth is usually the dimension perpendicular to the plane the figure is drawn in.
Height
Height is also used as a term for distance measured in a third dimension perpendicular to both length and breadth.
However, whereas depth has connotations of down, height is used for distances up from the plane.
Euclidean Definition
When discussing the size and shape of a general polygon, the words height and width are often seen.
In this context, the height of the rectangle is the length going up the page, the width going across the page.
As Euclid defined it:
- The height of any figure is the perpendicular drawn from the vertex to the base.
(The Elements: Book VI: Definition $4$)
See Height of a Polygon.
Extract the definition of height and from the various places it has been defined, and put it in its own Euclid-specific page.
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Distance
The term distance has a specialized meaning in analysis which has an immediate practical application in analytic geometry.
