Drawing the fundamental domain with TeX

Question

I am new to using TeX as a tool to draw something, I am just familiar with typing formulas etc.

How can I draw the fundamental domain of the action of the special linear group acting on the upper half plane?

Answer 1

• The basic TikZ command for this type of diagram is \draw.

• Straight lines require just the coordinates (a,b)--(c,d). Default unit is 1cm. Rectangular (x,y) or polar (θ:r) coordinates can be used. Circular arcs are drawn using the arc(θ₁:θ₂:radius) option.

• Line thickness can be selected from a variety of options such as thin (the default), thick, very thick, etc., or be set to any width you choose.

• Line styles include dashed, dotted and many others.

• Text elements (including math using $..$) can be added using node[options]{text}

• The fill option will fill the drawn region with the selected color.

• The \path command is just like \draw except the path is invisible.

• There are many, many more options but this should get you started.

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[scale=3]
\draw[densely dashed] (1,0) arc (0:60:1) (-1,0) arc (180:120:1);
\draw[very thick, fill=gray!30] (.5,1.5) --node[right, pos=.9]{$e^{2\pi i/6}=\rho$} (60:1) arc (60:120:1)
    --node[left, pos=.1]{$\rho^2=e^{2\pi i/3}$} (-.5,1.5);
\draw[-latex] (-1.2,0) -- (1.2,0)node[below]{Re};
\draw[-latex] (0,-.2) -- (0,1.7)node[right]{Im};
\path(-1,0) --node[below, pos=0]{$-1$}node[below right, pos=.5]{0}node[below, pos=1]{1} (1,0)
    (0,1)node[below right]{$i$};
\draw(-.5,.02)--(-.5,-.02)node[below]{$-\frac{1}{2}$}(.5,.02)--(.5,-.02)node[below]{$\frac{1}{2}$};
\end{tikzpicture}

\end{document}