Improved knot table

This commit is contained in:
Mark 2023-05-05 14:53:42 -07:00
parent 3e16019521
commit 19335875e4
6 changed files with 19 additions and 28 deletions

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@ -1,9 +1,10 @@
\section{Table of Prime Knots}
A knot's \textit{crossing number} is the minimal number of crossings its projection must contain. In general, it is very difficult to determine a knot's crossing number.
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 15 smallest prime knots, ordered by crossing number. \par
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
@ -11,39 +12,29 @@ Mirror images are not included, even if the mirror image produces a nonisomorphi
% Images are from the appendix of the Knot book.
{
\def\w{24mm}
\foreach \l/\c/\r 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}%
\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/\l.png} \par
\includegraphics[width=\linewidth]{knot table/\a.png} \par
\vspace{2mm}
{\huge $\l$}
{\huge $\a$}
\end{center}
\end{minipage}
\hfill
\begin{minipage}{\w}
\begin{center}
\includegraphics[width=\linewidth]{knot table/\c.png} \par
\vspace{2mm}
{\huge $\c$}
\end{center}
\end{minipage}
\hfill
\begin{minipage}{\w}
\begin{center}
\includegraphics[width=\linewidth]{knot table/\r.png} \par
\vspace{2mm}
{\huge $\r$}
\end{center}
\end{minipage}
\hfill~\par
\vspace{4mm}
\ifnum\value{knotcounter}=4
\hfill~\par
\vspace{4mm}
\setcounter{knotcounter}{0}
\fi
}
}