Example: Borromean rings

% Title: Borromean_rings
% Author: Dan Drake <http://math.kaist.ac.kr/~drake>
% This document shows how to make the Borromean rings using TikZ. It's
% not very complicated, but it shows you how much a TikZ picture is
% really just like some source code.
%
% This document may be distributed and modified under the terms of the
% Creative Commons Attribution-Share Alike 3.0 license. See
% http://creativecommons.org/licenses/by-sa/3.0/.
%
% This document is available from
% http://www.scribd.com/doc/3292620/Borromean-rings. The
% LaTeX{} source code is available from http://math.kaist.ac.kr/~drake.

\documentclass{article}
\usepackage{tikz}
% drawing parameters
\newcommand{\circdist}{1}  % distance from origin to center of circles
\newcommand{\circrad}{7/4} % radius of the circles
\newcommand{\circlethickness}{6mm} % uh, thickness of the circles

% distance from the origin to the three "interior" intersections
\pgfmathsetmacro{\intrad}{sqrt((\circrad)^2 - 3*(\circdist)^2/4) - \circdist/2}

% distance from the origin to the three "exterior" intersections
\pgfmathsetmacro{\extrad}{sqrt((\circrad)^2 - 3*(\circdist)^2/4) + \circdist/2}

% so we can just specify an angle and get the correct color for the circle
\colorlet{180}{blue}
\colorlet{60}{red}
\colorlet{300}{green}

% draws one of our circles
\newcommand{\mycircle}[1]{%
  \draw[thick, double distance=\circlethickness, double=#1]
  (#1:\circdist) circle (\circrad);}

\begin{document}

\begin{center}
\begin{tikzpicture}[scale=2]
  % draw the circles
  \foreach \angle in {180, 60, 300}
  {
    \mycircle{\angle}
  }

  % we need to re-do two of the intersections so that the rings
  % interlock and aren't just piled on top of one another
  \foreach \angle/\rad in {60/\intrad, 240/\extrad}
  {
    \begin{scope}
      \clip (\angle:\rad) circle (5/4*\circlethickness);
      %                          you may need to adjust the 5/4 above so
      %                          the clipping area is big enough
      \mycircle{300}
      \mycircle{180}
    \end{scope}
  }
\end{tikzpicture}
\end{center}

\end{document}