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'length'
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| Title of object: |
length |
| Canonical Name: |
BasicLength |
| Type: |
Definition |
| Created on: |
2007-01-02 16:35:49 |
| Modified on: |
2007-06-06 15:58:16 |
| Classification: |
msc:51-00, msc:51D20 |
Revision comment (for changes between this and next version):
"dimension" is not a good link
rewording for "dimension" avoidance
emphasizing "length" when assigned a new definition
adding "length of a polygon" and "length of a set" in the defines section |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
% as suggested by Wkbj79
\usepackage{pstricks} |
Content:
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.
In two-dimensional space, length usually goes along the $x$ axis while height goes along the $y$ axis. The same holds for three-dimensional space.
For triangles, pentagons, and higher \PMlinkname{$n$-gons}{Polygon}, it is customary to refer to the dimension of any side as its length. 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. |
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