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length (Definition)

The length of a line segment is the distance between its endpoints. Length may be measured in meters, yards, abstract units, etc. For example, in the following diagram


\begin{pspicture}(-1,-0.3)(13,0.3) \psline{<->}(-1,0)(13,0) \psdots(0,0)(3,0)(9,... ...){$D$} \rput[b](12,0.2){$E$} \rput[l](-1,0){.} \rput[r](13,0){.} \end{pspicture}

$AB$ is one unit long, $BC$ is two units long, $CD$ is a fifth of a unit, $DE$ is four fifths of a unit, $AC$ is three units, etc.

The concept of length as defined above is a special case of a general concept called measure.

In two-dimensional space, length usually goes along the $x$ axis while height goes along the $y$ axis. The same holds in three-dimensional space.

For triangles, pentagons, and higher $n$ -gons, it is customary to refer to the length of any of its sides as the length of the polygon. The length of a circle's side is called its circumference.

In set theory, length refers to the number of elements a set (or one-dimensional array) has. This is also known as cardinality. For example, $\{2, 5, 11, 23, 47\}$ has length $5$ .




"length" is owned by PrimeFan. [ full author list (2) | owner history (1) ]
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See Also: area, volume, polygon

Also defines:  length of a polygon, length of a set
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Cross-references: cardinality, number, set theory, circumference, circle's, sides, pentagons, triangles, height, axis, measure, diagram, units, endpoints, distance, line segment
There are 117 references to this entry.

This is version 14 of length, born on 2007-01-02, modified 2007-10-20.
Object id is 8709, canonical name is BasicLength.
Accessed 5589 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )
 51M25 (Geometry :: Real and complex geometry :: Length, area and volume)
 51D20 (Geometry :: Geometric closure systems :: Combinatorial geometries)

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