\documentclass[a4paper]{report}
\usepackage[dvips]{graphics}
\begin{document}
  \title{Polar Fishing}
  \author{S. Kimo\\
          McGills University\\
          Canada  
      \and R. Poon\\
          University of Whales\\
          U.K.}
  \date{Version 3.2: \today}
  \maketitle
\chapter{Introduction}\label{ch:int}

A \emph{folium} is a generic term for a leaf--shaped curve.  According
to Lawrence~\cite[page 151]{Law}, the curve defined by the equation
\begin{equation}\label{eq:f}
  \left(x^2+y^2\right)\left(y^2 + x(x+b)\right) = 4axy^2
\end{equation}
was known to Kepler in 1609 and generates a Simple--, Double-- or
Tri--Folium, when $b \ge 4a$, $b = 0$ or $0 < b < 4a$, respectively.
\section{Reparameterization}
To draw the folium defined by equation (\ref{eq:f}) in
Chapter~\ref{ch:int} it is convenient to change to polar coordinates 
$x = r(\theta)\cos\theta$ and $y = r(\theta)\sin\theta$.  This leads to
\begin{equation}
  r(\theta) = -b\cos\theta + 4a\cos\theta\sin^2\theta,
\end{equation}
for $0 \le \theta <2\pi$ and is illustrated on the left of
Figure~\ref{fig:f} for the values $a=1$, $b=2$.
\begin{figure}[!bp]
  \centering
  \scalebox{.35}{%
     \includegraphics{Folium2.eps}}
  \caption{Left: The Tri--folium for $a=1$, $b=2$, Right: a related curve.}
  \label{fig:f}
\end{figure}
\appendix
\chapter{A Related Curve}
A curve of a similar Tri--folium shape is defined~\cite[page 168]{Wie}
by the equation
\begin{equation}
x^4+y^4 + x(x^2-y^2)=0
\end{equation}
and is shown on the right of Figure~\ref{fig:f}.
\begin{thebibliography}{9}
  \bibitem{Law} J.~D.~Lawrence, \emph{A Catalog of Special Plane
              Curves}, Dover Publications, New York, 1972.
  \bibitem{Wie} Heinrich Wieleitner, \emph{Theorie der ebenen
               algebraischen Kurven h\"{o}herer Ordnung},
              G.~J.~G\"{o}schensche Verlangshandlung, Leipzig, 1905.
\end{thebibliography}
\end{document}