51 lines
1.1 KiB
TeX
51 lines
1.1 KiB
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. In general, it is very difficult to determine a knot's crossing number.
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\vspace{1mm}
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This table contains the 15 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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\foreach \l/\c/\r in {%
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{3_1}/{4_1}/{5_1},%
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{5_2}/{6_1}/{6_2},%
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{6_3}/{7_1}/{7_2},%
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{7_3}/{7_4}/{7_5},%
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{7_6}/{7_7}/{8_1}%
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}{
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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/\l.png} \par
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\vspace{2mm}
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{\huge $\l$}
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\end{center}
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\end{minipage}
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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/\c.png} \par
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\vspace{2mm}
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{\huge $\c$}
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\end{center}
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\end{minipage}
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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/\r.png} \par
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\vspace{2mm}
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{\huge $\r$}
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\end{center}
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\end{minipage}
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\hfill~\par
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\vspace{4mm}
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}
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}
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\vfill
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\pagebreak |