handouts/Advanced/Knots/parts/table.tex

\section{Table of Prime Knots}
A knot's \textit{crossing number} is the minimal number of crossings its projection must contain. \par
Finding a knot's crossing number is a fairly difficult problem.

\vspace{1mm}

This table contains the a 20 smallest prime knots, ordered by crossing number. \par
Mirror images are not included, even if the mirror image produces a nonisomorphic knot.

\vfill

% Images are from the appendix of the Knot book.
{
	\def\w{24mm}
	\newcounter{knotcounter}

	\foreach \a in {%
		{3_1},{4_1},{5_1},{5_2},%
		{6_1},{6_2},{6_3},{7_1},%
		{7_2},{7_3},{7_4},{7_5},%
		{7_6},{7_7},{8_1},{8_2},%
		{8_3},{8_4},{8_5},{8_6}%
	}{
		\stepcounter{knotcounter}
		\hfill
		\begin{minipage}{\w}
		\begin{center}
			\includegraphics[width=\linewidth]{knot table/\a.png} \par
			\vspace{2mm}
			{\huge $\a$}
		\end{center}
		\end{minipage}
		\ifnum\value{knotcounter}=4
			\hfill~\par
			\vspace{4mm}
			\setcounter{knotcounter}{0}
		\fi
	}
}

\vfill
\pagebreak