I saw a question on X/Twitter by とと about drawing certain circles, partially filled, together with aligned equations. So, I quickly wrote some TikZ code to demonstrate how such drawings can be done.

This is the result:

And this is the code:

\documentclass[tikz]{standalone} \usetikzlibrary{positioning} \usepackage{amsmath} \begin{document} \begin{tikzpicture}[dot/.style={circle, fill, inner sep = 1.3pt}] \draw node[dot, label = below:$z_0$] (z0) {}; \draw node[dot, label = below:$z_1$, below left = 1 and 2.4 of z0] {}; \begin{scope}% scope of clipping \clip circle (0.6) (-4,-3) rectangle (4,3); \filldraw[dashed,fill=gray!30] circle (1.8); \draw [dashed] circle (0.6) circle (2.5); \end{scope} \draw [rotate=90] (-0.72,-0.2) ++(270:2.5) arc (-30:30:5.4) ; \draw [rotate=90] (-0.05,-0.3) ++(270:2.5) arc (-30:30:5.6) ; \node [anchor=north west] at (2.75,0.1) {$\begin{aligned} \varphi(z) &= a > \varphi(z_0)\\ \varphi(z) &= \varphi(z_0)\\ \\ \varphi(z) &\leq \varphi(z_0) \end{aligned}$}; \draw [->] (2.7,-1.3) -- ++ (270:1); \end{tikzpicture} \end{document}

To be fast, for positioning, I estimated many coordinates and adjusted them so the result looks good.

Learning TikZ is challenging but really rewarding. A good book can help learning the basics quickly, such as TikZによるLaTeXグラフィックス.