% This picture represents the universal convering of the unit circle
% (C) Thiago Brevidelli
\begin{tikzpicture}[scale=0.75]
\begin{scope}[shift={(-3.5, -2.75)}]
    \begin{axis}[
        view={0}{60}, 
        axis lines=none, 
        ymin=-2, 
        ymax=.5, 
        xmin=-1, 
        xmax=1
      ]
        \addplot3[
          very thick, 
          domain=-1.25*pi:6.25*pi, 
          samples = 200, 
          samples y=0
        ] 
          ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x});
    
        \addplot3[
          very thick, 
          dotted, 
          domain=-1.5*pi:-1.25*pi, 
          samples = 200, 
          samples y=0
        ] 
          ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x});
    
        \addplot3[
          very thick, 
          dotted, 
          domain=6.25*pi:6.5*pi, 
          samples = 200, 
          samples y=0
        ] 
          ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x});
    \end{axis}
\end{scope}

\draw[thick, ->] (0, 0) -- node[right]{$\pi$} (0, -1);
\draw[thick] (0, -1.5) ellipse (0.9 and 0.25);
\end{tikzpicture}
