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'symmetry'
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| Title of object: |
symmetry |
| Canonical Name: |
Symmetry2 |
| Type: |
Definition |
| Created on: |
2007-06-04 21:39:42 |
| Modified on: |
2007-06-05 09:56:47 |
| Classification: |
msc:51A15, msc:51A10, msc:15A04 |
| Defines: |
symmetry about, symmetric, symmetric about, rotational symmetry, point symmetry, symmetry about a point, symmetric about a point, reflectional symmetry, line symmetry, symmetry about a line, symmetric about a line |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{pstricks}
\usepackage{psfrag}
\usepackage{graphicx}
\usepackage{amsthm}
\usepackage{xypic}
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Content:
\PMlinkescapeword{terms}
\PMlinkescapetext{This entry is not yet complete.}
Let $V$ be a Euclidean vector space, $F \subseteq V$, and $E \colon V \to V$ be a Euclidean transformation.
The following terms are used to indicate that $E(F)=F$ if $E$ is a rotation:
\begin{itemize}
\item $F$ has \emph{rotational symmetry};
\item $F$ has \emph{point symmetry};
\item $F$ has \emph{symmetry about a point};
\item $F$ is \emph{symmetric about a point}.
\end{itemize}
\PMlinkescapetext{Picture in the case of} $V=\mathbb{R}^2$ \PMlinkescapetext{will be added.}
\PMlinkescapetext{How to determine $E$ for a specific point $x$ will be added.}
If $E(F)=F$ and $E$ is a reflection, then $F$ has \emph{reflectional symmetry}. In the special case that $V=\mathbb{R}^2$, the following terms are used:
\begin{itemize}
\item $F$ has \emph{line symmetry};
\item $F$ has \emph{symmetry about a line};
\item $F$ is \emph{symmetric about a line}.
\end{itemize}
\PMlinkescapetext{Picture in the case of} $V=\mathbb{R}^2$ \PMlinkescapetext{will be added.}
\PMlinkescapetext{How to determine $E$ for a specific line $\ell$ will be added.}
\PMlinkescapetext{Feel free to add these before I do if you wish!} |
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