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} \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} \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. Mirror images are not included, even if the mirror image produces a nonisomorphic knot.
\vfill \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. % Images are from the appendix of the Knot book.
{ {
\def\w{24mm} \def\w{24mm}
\foreach \l/\c/\r in {% \newcounter{knotcounter}
{3_1}/{4_1}/{5_1},%
{5_2}/{6_1}/{6_2},% \foreach \a in {%
{6_3}/{7_1}/{7_2},% {3_1},{4_1},{5_1},{5_2},%
{7_3}/{7_4}/{7_5},% {6_1},{6_2},{6_3},{7_1},%
{7_6}/{7_7}/{8_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 \hfill
\begin{minipage}{\w} \begin{minipage}{\w}
\begin{center} \begin{center}
\includegraphics[width=\linewidth]{knot table/\l.png} \par \includegraphics[width=\linewidth]{knot table/\a.png} \par
\vspace{2mm} \vspace{2mm}
{\huge $\l$} {\huge $\a$}
\end{center} \end{center}
\end{minipage} \end{minipage}
\hfill \ifnum\value{knotcounter}=4
\begin{minipage}{\w} \hfill~\par
\begin{center} \vspace{4mm}
\includegraphics[width=\linewidth]{knot table/\c.png} \par \setcounter{knotcounter}{0}
\vspace{2mm} \fi
{\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}
} }
} }