how to insert DENSELY dashdotted line in math mode or equations?

Question

\documentclass[12pt,a4paper,onecolumn]{article}
\usepackage{tikz}
\usepackage{caption}
\usetikzlibrary{positioning,fit,calc}

\begin{document}
\tikzstyle{every node}=[circle, draw, fill=black!100,
                       inner sep=0pt, minimum width=6pt]
\begin{tikzpicture}[thick,scale=0.8]%
\draw(0,0)node[label={[yshift=0cm]270:{$1$}}](1){};
\draw(0,4)node[label={[yshift=0cm]90:{$2$}}](2){};
\draw(4,4)node[label={[yshift=0cm]90:{$3$}}](3){};
\draw(4,0)node[label={[yshift=0cm]270:{$4$}}](4){};

\draw[->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](1)--(2);
\draw[dashed, ->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](2)--(3);
\draw[densely dotted,->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](3)--(4);
\draw[densely dashdotdotted, ->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](4)--(1);
\end{tikzpicture}
{\captionof{figure}{4 types of arcs.}}

In Figure 1, there are 4 types of arcs, namely the solid $<display Solid Line Here>$, dashed $<display Dashed Line Here>$, densely dotted $<display Densely Dotted Line Here>$, and densely dashdotdotted $<display Densely Dashdotdotted Line Here>$.
\noindent\par The best I can do is 
In Figure 1, there are 4 types of arcs, namely the solid $<display Solid Line Here>$, dashed $<--->$, densely dotted $<\cdots>$, and densely dashdotdotted $<display Densely Dashdotdotted Line Here>$
\end{document}

Thank you

Answer 1

You can insert TikZ pictures at almost arbitrary locations in your document. There is even the shorthand notation \tikz...; for inline pictures with a single path.

To get a nice centering on the line I used baseline=-\the\fontdimen22\textfont2 which is the height at which operators will be centered in math mode. See also What do different \fontdimen<num> mean

\documentclass[12pt,a4paper,onecolumn]{article}
\usepackage{tikz}
\usepackage{caption}
\usetikzlibrary{positioning,fit,calc}
\begin{document}
\begin{center}
  \begin{tikzpicture}[
    thick,
    scale=0.8,
    every node/.style={
      circle,
      draw,
      fill=black!100,
      inner sep=0pt,
      minimum width=6pt
    }]
    \draw(0,0)nodelabel={[yshift=0cm]270:{$1$}}{};
    \draw(0,4)nodelabel={[yshift=0cm]90:{$2$}}{};
    \draw(4,4)nodelabel={[yshift=0cm]90:{$3$}}{};
    \draw(4,0)nodelabel={[yshift=0cm]270:{$4$}}{};
\draw[->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](1)--(2);
\draw[dashed, ->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](2)--(3);
\draw[densely dotted,->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](3)--(4);
\draw[densely dashdotdotted, ->, line width=0.3mm, >=latex, shorten <= 0.2cm, shorten >= 0.15cm](4)--(1);

\end{tikzpicture}
  \captionof{figure}{\label{fig:arcs}4 types of arcs.}
\end{center}
\newcommand*\lineexample[1]{%
  #1~(\tikz[baseline=-\the\fontdimen22\textfont2]\draw#1--(1.618em,0);)%
}
In Figure~\ref{fig:arcs}, there are 4 types of arcs, namely the
\lineexample{solid}, \lineexample{dashed}, \lineexample{densely dotted}, and
\lineexample{densely dashdotdotted}.
\end{document}

---

Just for fun, here is the same example again with \graph.

\documentclass[12pt,a4paper,onecolumn]{article}
\usepackage{tikz}
\usetikzlibrary{graphs}
\begin{document}
\begin{figure}
  \centering
  \begin{tikzpicture}[
    thick,
    scale=0.8,
    every node/.style={
      circle,
      draw,
      fill=black!100,
      inner sep=0pt,
      minimum width=6pt
    }]
\node[label={below:$1$}](1) at (0,0) {};
\node[label={above:$2$}](2) at (0,4) {};
\node[label={above:$3$}](3) at (4,4) {};
\node[label={below:$4$}](4) at (4,0) {};

\graph [use existing nodes,edges={>=latex,shorten <=0.2cm,shorten >=0.15cm}] {
  1 ->[solid] 2 ->[dashed] 3 ->[densely dotted] 4 ->[densely dashdotted] 1
};

\end{tikzpicture}
  \caption{\label{fig:arcs}4 types of arcs.}
\end{figure}
\newcommand*\lineexample[1]{%
  #1~(\tikz[baseline=-\the\fontdimen22\textfont2]\draw#1--(1.618em,0);)%
}
In Figure~\ref{fig:arcs}, there are 4 types of arcs, namely the
\lineexample{solid}, \lineexample{dashed}, \lineexample{densely dotted}, and
\lineexample{densely dashdotted}.
\end{document}