42 lines
972 B
TeX
42 lines
972 B
TeX
\section{Table of Prime Knots}
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A knot's \textit{crossing number} is the minimal number of crossings its projection must contain. \par
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Finding a knot's crossing number is a fairly difficult problem.
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\vspace{1mm}
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This table contains the a 20 smallest prime knots, ordered by crossing number. \par
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Mirror images are not included, even if the mirror image produces a nonisomorphic knot.
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\vfill
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% Images are from the appendix of the Knot book.
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{
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\def\w{24mm}
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\newcounter{knotcounter}
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\foreach \a in {%
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{3_1},{4_1},{5_1},{5_2},%
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{6_1},{6_2},{6_3},{7_1},%
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{7_2},{7_3},{7_4},{7_5},%
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{7_6},{7_7},{8_1},{8_2},%
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{8_3},{8_4},{8_5},{8_6}%
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}{
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\stepcounter{knotcounter}
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\hfill
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\begin{minipage}{\w}
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\begin{center}
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\includegraphics[width=\linewidth]{knot table/\a.png} \par
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\vspace{2mm}
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{\huge $\a$}
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\end{center}
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\end{minipage}
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\ifnum\value{knotcounter}=4
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\hfill~\par
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\vspace{4mm}
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\setcounter{knotcounter}{0}
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\fi
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}
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}
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\vfill
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\pagebreak |