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\title{General Mathematics and CPS II}
\author{Exercise 10}
\date{March 7, 2014}
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\begin{enumerate}

\item (Ivanov, p. 41, Exercise.)  Let $R_\alpha$ denote the reflection
about the line $x=\alpha$.  Let $G$ be the (symmetry) group generated
by the unit translation along the $x$-axis and by $R_0$.  Show that
$R_\alpha \in G$ if and only if $2 \alpha \in \mathbb{Z}$.

\item Using the notation of the previous question, show that if $G$ is
generated by $H$, the point symmetry about the origin, and by
$R_\alpha$, then we must have $4\alpha \in \mathbb Z$ and the
situation reduces to one of the seven cases considered in class.
(Which one?)

\item Draw an ornament corresponding to each of the seven cases
considered in class.  Make sure that each example has precisely the
symmetries of the respective case, and no more.


\end{enumerate}


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