TeX for drawing circles with inscribed polygons and labeled vertices, for the Josephus problem.

readme.md

Circle with inscribed polygon, for illustrating the Josephus permutation:

poly_circ_undirected.tex

\documentclass[border=2mm]{standalone}
\usepackage{tikz}
\usepackage{xintexpr}
\usetikzlibrary{shapes.geometric}

\begin{document}
\begin{tikzpicture}[scale=3]

% make a node with variable name pol (with the list of features given) at the location (0,0), and don't label it
\node (pol) [draw=none, thick, black!90!black,rotate=0,minimum size=6cm,regular polygon, regular polygon sides=11] at (0,0) {}; 


% anchor is "corner 1"
% label is 1/2/3/4/etc
% placement is placement w.r.t. coordinate location
\foreach \anchor/\label/\placement in
    {corner 1/$1$/above, 
     corner 2/$2$/above left, 
     corner 3/$3$/left, 
     corner 4/$4$/left,
     corner 5/$5$/below left,   
     corner 6/$6$/below,
     corner 7/$7$/below,
     corner 8/$8$/below right,
     corner 9/$9$/right,
     corner 10/${10}$/right,
     corner 11/${11}$/above right}
\draw[shift=(pol.\anchor)] plot coordinates{(0,0)} node[font=\scriptsize,\placement] {\label};

% solution for n = 11, m = 4:
% ( 1 3 7 6 4 ) ( 2 8 ) ( 5 9 11 ) ( 10 )

% internal paths

% cycle (1 3 7 6 4)
\path [-] (pol.corner 1) edge (pol.corner 3);
\path [-] (pol.corner 3) edge (pol.corner 7);
\path [-] (pol.corner 7) edge (pol.corner 6);
\path [-] (pol.corner 6) edge (pol.corner 4);
\path [-] (pol.corner 4) edge (pol.corner 1);

% cycle 2 (2 8)
\path [-] (pol.corner 2) edge (pol.corner 8);
\path [-] (pol.corner 8) edge (pol.corner 2);

% cycle 3 (5 9 11 )
\path [-] (pol.corner 5) edge (pol.corner 9);
\path [-] (pol.corner 9) edge (pol.corner 11);
\path [-] (pol.corner 11) edge (pol.corner 5);


% draw a circle connecting all points
\draw circle[radius=1.01cm];


% Draw a red dot at the starting point 
\filldraw[red] (pol.corner 1) circle[radius=0.8pt];

% optional: black dots at each circle location
\filldraw[black] (pol.corner 2) circle[radius=0.4pt];
\filldraw[black] (pol.corner 3) circle[radius=0.4pt];
\filldraw[black] (pol.corner 4) circle[radius=0.4pt];
\filldraw[black] (pol.corner 5) circle[radius=0.4pt];
\filldraw[black] (pol.corner 6) circle[radius=0.4pt];
\filldraw[black] (pol.corner 7) circle[radius=0.4pt];
\filldraw[black] (pol.corner 8) circle[radius=0.4pt];
\filldraw[black] (pol.corner 9) circle[radius=0.4pt];
\filldraw[black] (pol.corner 10) circle[radius=0.4pt];
\filldraw[black] (pol.corner 11) circle[radius=0.4pt];

\end{tikzpicture}
\end{document}