\documentclass[11pt,oneside]{amsart}
\usepackage{amssymb, amsmath, amsthm}

\usepackage{epsfig}
\usepackage{epstopdf}
\usepackage{graphicx}
\usepackage{color}
%\usepackage[shortalphabetic]{amsrefs}
\usepackage{mathptmx}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
%\usepackage{url}

%\usepackage{pinlabel}

%Define theorem styles
     \theoremstyle{definition}
      \newtheorem{theorem}{Theorem}[section]
      \newtheorem*{theorem*}{Theorem}
      \newtheorem{definition}[theorem]{Definition}
      \newtheorem{exercise}[theorem]{Exercise}
      \newtheorem{example}[theorem]{Example}
      \newtheorem{conj}{Conjecture}
      \newtheorem{proposition}[theorem]{Proposition}
      \newtheorem{corollary}[theorem]{Corollary}
      \newtheorem{claim}{Claim}
      \newtheorem{lemma}[theorem]{Lemma}
    
   % Define new commands

      \newcommand{\R}{{\mathbb R}}
      \newcommand{\C}{\mathbb C}
      \newcommand{\Z}{\mathbb Z}
	\newcommand{\N}{\mathbb N}
	\newcommand{\Q}{\mathbb Q}
	\newcommand{\Hy}{\mathbb H}
	\newcommand{\E}{\mathbb E}
      \newcommand{\nil}{\varnothing}
	\newcommand{\til}{\tilde}
	\newcommand{\boundary}{\partial}
	\newcommand{\m}{\backslash}
	\newcommand{\mc}[1]{\mathcal{#1}}
	\newcommand{\vect}[1]{\mathbf{#1}}
	\newcommand{\prob}[1]{\textbf{Problem {#1}: }}
	\newcommand{\defn}[1]{\textbf{#1}}
	\newcommand{\ob}[1]{\overline{#1}}
	%\newcommand{\ker}{\operatorname{ker}}
	\newcommand{\im}{\operatorname{im}}
	\newcommand{\tr}{\operatorname{tr}}
	\newcommand{\rank}{\operatorname{rank}}
	\newcommand{\rref}{\operatorname{rref}}
	\newcommand{\hyp}{\text{hyp}}
	
	\newcommand{\diver}{\operatorname{div}}
	\newcommand{\curl}{\operatorname{curl}}
	\newcommand{\grad}{\operatorname{grad}}

	\newcommand{\lpartial}[1]{\frac{\partial}{\partial #1}}
	\newcommand{\llpartial}[2]{\frac{\partial #1}{\partial #2}}
	\newcommand{\co}{\mskip0.5mu\colon\thinspace} 
	\newcommand{\spacing}{\parskip 6.6pt
\parindent 0pt}

	\newcommand{\custthm}[2]{
			\framebox[0.95\linewidth]{
			\begin{minipage}{0.9\linewidth}

			\begin{theorem}\label{#1}
			#2	
			\end{theorem}
			\end{minipage}
			}
	}
	
	
	
	\newenvironment{enumer}
		{\begin{enumerate}
		\parskip 6.6pt
		\parindent 0pt
		\renewcommand{\labelenumi}{(\alph{enumi})}
		
		}
		{\end{enumerate}}


	  
\parskip 6.6pt
\parindent 0pt

%\renewcommand{\labelenumi}{(\alph{enumi})}


	
   % The following mysterious maneuver gets rid of AMS junk at the top
   % and bottom of the first page.
   
      \makeatletter
      \def\@setcopyright{}
      \def\serieslogo@{}
      \makeatother
   
% This ends the preamble.  We now proceed to the document itself.

\begin{document}


   % title

   \title[short title]{long title}
   \author{}
   % Note that the short title for running heads goes in square
   % brackets.  This is optional.  The long title goes in curly
   % braces.  In the long title, line breaks are indicated by \\.


%Here are two sets of commands for including images.
  
%\begin{center}
%\begin{figure}[h]
%\includegraphics[scale=0.4]{FinalExam-prob10.pdf}
%\end{figure}
%\end{center}

%\begin{figure}[ht] 
%\scalebox{0.5}{\input{Pen.eps_t}}
%\caption{A pox on both your houses!}
%\end{figure}

   

   % today's date, or fill in whatever date you prefer
   \date{\today}

\framebox{
\raisebox{0in}[.5in][.2in]{
\textbf{MA 314 Homework 9: ``Orthogonal Circles'' would be a great name for a band.} 
}
}

This homework is intended to be lighter than usual.

\section{Reading}
Read the following sections on hyperbolic geometry:
\begin{itemize}\spacing
\item Bonahon: Section 2.5 - 2.7 (In section 2.6, just pay attention to the notation for now.)
\item Schwartz: Sections 10.4 and 10.7
\item Watch the \href{http://www.ima.umn.edu/videos/mobius.php}{video on M\"obius transformations} by Douglas Arnold and Jonathan Rogness.
\end{itemize}
\section{Mortar}
\begin{itemize}\spacing
\item In class we sketched a proof of Lemma 2.8 (Bonahon) and how it can be used to show that every isometry of $\Hy^2$ is a linear fractional transform or anti-linear fractional transform. Write out the whole proof, filling in all the details (especially those omitted by Bonahon). Conclude by describing how this result is used to show that every isometry of $\Hy^2$ is the composition of basic isometries.

\item Do Exercise 2.9 of Bonahon on page 41. (Hint: Use the result proved in class that a hyperbolic isometry which fixes 3 points not on a geodesic is the identity, but remember that 0 and $\infty$ are not elements of $\Hy^2$.)

\end{itemize}




\end{document}