\documentclass[a4paper]{article}
\usepackage[dvips]{graphics} 
\begin{document}
  \title{Polar Fishing}
  \author{S. Kimo \and R. Poon}
  \date{Version 3.2: \today}
  \maketitle
\section{Introduction}\label{sec:int}

A \emph{folium} is a generic term for a leaf--shaped curve.  According
to Lawrence~\cite[page 151]{Law}, the curve defined implicitly 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.
 
\subsection{Reparameterization}

To draw the folium defined by equation (\ref{eq:f}) in
Section~\ref{sec:int} it is convenient to change to polar coordinates
$x = r(\theta)\cos\theta$ and $y = r(\theta)\sin\theta$.  This leads to
\[
  r(\theta) = -b\cos\theta + 4a\cos\theta\sin^2\theta,
\]
for $0 \le \theta <2\pi$ and is illustrated in Figure~\ref{figa} for
$a=1$, $b=2$.

\begin{figure}[!hp]
  \centering
    \scalebox{.23}{%	       
       \includegraphics{Folium.eps}
                 }
  \caption{The Tri--folium for $a=1$, $b=2$.}
  \label{figa}
\end{figure}

\paragraph{Acknowledgements}
The definition of the folium was taken from the World Wide Web page
titled ``Famous Curves Index'' that may be found at the address

\verb+http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html+
\noindent
It contains pictures of this and many other curves.
\begin{thebibliography}{9}
  \bibitem{Law} J.~D.~Lawrence, \emph{A Catalog of Special Plane
                          Curves}, Dover Publications, New York, 1972.
\end{thebibliography}

\end{document}