lengthBasicLength2007-01-02 16:35:492007-10-20 03:45:41Definitionlength of a polygonlength of a set% this is the default PlanetMath preamble. as your knowledge
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\usepackage{pstricks}The \emph{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{center}
\begin{pspicture}(-1,-0.3)(13,0.3)
\psline{<->}(-1,0)(13,0)
\psdots(0,0)(3,0)(9,0)(9.6,0)(12,0)
\rput[a](0,-0.3){0}
\rput[a](3,-0.3){1}
\rput[a](9,-0.3){3}
\rput[a](9.6,-0.3){3.2}
\rput[a](12,-0.3){4}
\rput[b](0,0.2){$A$}
\rput[b](3,0.2){$B$}
\rput[b](9,0.2){$C$}
\rput[b](9.6,0.2){$D$}
\rput[b](12,0.2){$E$}
\rput[l](-1,0){.}
\rput[r](13,0){.}
\end{pspicture}
\end{center}
$AB$ 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 \PMlinkname{$n$-gons}{BasicPolygon}, it is customary to refer to the length of any of its sides as the \emph{length of the \PMlinkescapetext{polygon}}. The length of a circle's side is called its circumference.
In set theory, \emph{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 $5$.