diff --git a/Advanced/Knots/knot table/8_2.png b/Advanced/Knots/knot table/8_2.png new file mode 100644 index 0000000..4167758 Binary files /dev/null and b/Advanced/Knots/knot table/8_2.png differ diff --git a/Advanced/Knots/knot table/8_3.png b/Advanced/Knots/knot table/8_3.png new file mode 100644 index 0000000..7d60b61 Binary files /dev/null and b/Advanced/Knots/knot table/8_3.png differ diff --git a/Advanced/Knots/knot table/8_4.png b/Advanced/Knots/knot table/8_4.png new file mode 100644 index 0000000..b1d234b Binary files /dev/null and b/Advanced/Knots/knot table/8_4.png differ diff --git a/Advanced/Knots/knot table/8_5.png b/Advanced/Knots/knot table/8_5.png new file mode 100644 index 0000000..bc8ee74 Binary files /dev/null and b/Advanced/Knots/knot table/8_5.png differ diff --git a/Advanced/Knots/knot table/8_6.png b/Advanced/Knots/knot table/8_6.png new file mode 100644 index 0000000..1ac7418 Binary files /dev/null and b/Advanced/Knots/knot table/8_6.png differ diff --git a/Advanced/Knots/parts/table.tex b/Advanced/Knots/parts/table.tex index d3c24e9..9d87d54 100644 --- a/Advanced/Knots/parts/table.tex +++ b/Advanced/Knots/parts/table.tex @@ -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 } }