<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">
\def\Bbb{\mathbb}
\def\Haus{{\cal H}}
\def\dist{{\rm{dist}}}
\def\area{{\rm{area}}}
\def\dist{{\rm{dist}}}
\def\diam{{\rm{diam}}}
\def\dim{{\rm{dim}}}
\def\supp{{\rm{supp}}}
\def\Bbb{\mathbb}
\def\reals{\Bbb R}
\def\cal{\mathcal}
\newenvironment{pf}   {\begin{proof}}{\end{proof}}

 
\documentclass[12pt]{amsart}  % use this with LaTeX2e 
\usepackage{amssymb}    %use with LaTeX2e

%\UseAMSsymbols
%\documentstyle[12pt]{amsart} % use with AMS-LaTeX
 \input psfig     % use this package if postscript figures are to be added

\theoremstyle{plain}                    %------- 'regular' theorem types
\newtheorem{thm}{Theorem}[section]
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{example}[thm]{Example}
%\newtheorem{remark}[rem]{Remark}   
\newcounter{ques}
\newtheorem{ques}[thm]{Question}   
\numberwithin{equation}{section}
%\addtolength{\textwidth}{1in}         % increases text width
%\addtolength{\evenpagemargin}{-.5in}  % moves left margin 

%\addtolength{\textheight}{.80in}
\addtolength{\textwidth}{1.0in}
%\addtolength{\topmargin}{-.5in}
\addtolength{\leftmargin}{-.5in} 
\hoffset -.5in

\begin{document}
%\renewcommand{\baselinestretch}{2}
\baselineskip=18pt



%%%%%%%%%%%%%%%%%%   title  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  You don't need a title for homework
%\title []
%          {}

%\footnote{}
%\subjclass{Primary: Secondary: }
%\keywords{}
%\author {}
%\address{\\
%         Mathematics Department\\
%         SUNY at Stony Brook \\
%         Stony Brook, NY 11794-3651}
%\email {bishop@math.sunysb.edu}
%\thanks{The  author is partially supported by NSF Grant DMS .}
%\date
%\date{August 20, 2006}
%\maketitle

%%%%%%%%%%%%%%%%%%%%%%%% abstract %%%%%%%%%%%%%%%%%%%%%%%%

%\begin{abstract}
%\end{abstract}

%\clearpage

%%%%%%%%%%%%%%%%%%%%%%%% Introduction %%%%%%%%%%%%%%%%%%%%

\setcounter{page}{1}
\renewcommand{\thepage}{\arabic{page}}


%\section{Introduction}
%\subsection{}

%\begin{enumerate}
%\item 
%\end{enumerate}

{\bf Problem 0, Chapter 1, page 26:} Prove the circle is round.

\begin{proof}
This is  fairly clear from the formula 
$$ x^2+ y^2 =1,$$
and even more so from the complex form 
\begin{eqnarray*}
  |z|^2  &amp;=&amp;  (x+iy) \overline{(x+iy)} \\
         &amp;=&amp;  1 \\
         &amp;=&amp;  \frac {1+i}{2+i-1},
\end{eqnarray*}
or it can be observed in Figure \ref{fig1}:


\begin{figure}[htb]
\centerline{ 
\psfig{figure=sample.eps,height=2.0in}
 }
\caption{\label{fig1} This picture was created using 
    xfig and then exporting to postscript. It clearly 
    demonstrates the roundness of a circle and contrasts
      it to the non-roundness of a square.}
\end{figure}

\end{proof}


%\bibliography{weight}
%\bibliographystyle{plain}
\end{document}


\begin{comment}
    A comment is a way of preventing text from being 
included into the TeX form.  You can read this when 
you edit the file but it is invisible to TeX (and easier 
that putting the percent sign in front of every line.

\end{comment}
%=======================================================

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