There are some very well-known results and equations, e.g., Shanon Capacity formula, Erlang Distribution and Poisson Distribution, etc. Do we have to provide a reference for these results as well?

Also at times we seek help from a user manual while writing a simulation program or conducting a practical experiment. Do we have to provide reference for user manuals as well?


Question: How to construct a closed, filled, path made of semi-circles and attach annotations to it with TikZ?
Answer: Here is a quick attempt:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
  \draw[fill=blue] (0,0)node[below]{$A$} arc (0:180:6) node[below]{$B$};
  \draw (-12,0) - -(0,0);
  \draw[fill=white] (-8,0) arc (0:180:2);
  \draw[fill=white] (0,0) arc (0:180:4)node[below]{$P$};
  \draw (-6,-0.1) -- node[below]{$O$} (-6,0.1);
  \draw[&lt;-&gt;](-8,-0.6)--node[below]{$x$}(-6,-0.6);
  \draw[&lt;-&gt;](-6,-0.6)--node[below]{$6$}(0,-0.6);
\end{tikzpicture}

\end{document}


This produces:



Note that colouring/filling is cumulative: you can fill one region with a colour and then fill another overlapping region with a different colour, or white to remove the colour. The last colour in any given region wins.