|
|
|
Viewing Version
4
of
'equilateral polygon'
|
[ view 'equilateral polygon'
|
back to history
]
| Title of object: |
equilateral polygon |
| Canonical Name: |
EquilateralPolygon |
| Type: |
Definition |
| Created on: |
2007-06-05 14:12:23 |
| Modified on: |
2007-06-05 15:37:23 |
| Classification: |
msc:51-00 |
| Synonyms: |
equilateral polygon=equilateral |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{pstricks}
\usepackage{psfrag}
\usepackage{graphicx}
\usepackage{amsthm}
\usepackage{xypic}
|
Content:
A polygon is \emph{equilateral} if all of its sides are congruent.
Common examples of equilateral polygons are rhombi and regular polygons such as equilateral triangles and squares.
Let $T$ be a triangle. Then the following are equivalent:
\begin{itemize}
\item $T$ is equilateral;
\item $T$ is equiangular;
\item $T$ is regular.
\end{itemize}
If $T$ is allowed to be a polygon that has more than three sides, then the above statement is no longer true.
Below are some pictures of equilateral polygons that are not equiangular.
\begin{center}
\begin{pspicture}(0,0)(17,6)
\pspolygon(0,0)(3,2.25)(6.75,2.25)(3.75,0)
\pspolygon(7.5,0)(10.5,0)(10.5,3)(9,5.598)(7.5,3)
\pspolygon(11.268,1)(13,2)(15,2)(16.732,1)(15,0)(13,0)
\end{pspicture}
\end{center} |
|
|
|
|
|
