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\begin{document}

\noindent{\tiny mth 112}

\centerline{Using \Xy-pic}

\bigskip


Here is an attempt to draw a rational tangle $(p , q)$.  Amazingly enough, there is an extremely simple way to tell if two rational tangles are equivalent.  Suppose the two tangles are given by the sequences of integers $-2\  3\  2$ and $3\  {-2}\  3$.  We compute the so-called {\bf continued fractions} corresponding to these integers.  The continued fraction corresponding to $-2\  3\  2$ is produced by,





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\begin{figure}[ht]
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%\center{\includegraphics[scale=.5]{thesisfig1.png} }
\caption{A Rational Tangle}
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\vspace{1.5in}



\begin{figure}[ht]
$$ 2 + {1 \over 3 + (1/-2)}  $$
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\caption{Continued Fration}
\end{figure}







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