Hairy Ball Theorem

There is no non-vanishing smooth tangent vector field on even-dimensional $n$-spheres.

\begin{document} 
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               \draw[thick, blue] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={60:(-4,0)}] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={120:(-4,0)}] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={180:(-4,0)}] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={-60:(-4,0)}] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={-120:(-4,0)}] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={22.5:(-4,0)}, yshift = -1.5cm] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={-67.5:(-4,0)}, yshift = -1.5cm] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={20:(-4,0)}, yshift = -3cm, xshift=-1cm] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={-17.5:(-4,0)}, yshift = -2.5cm] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               \draw[thick, blue, rotate around={-150.5:(-4,0)}, yshift = -1.5cm] (-4,2.5) .. controls (-4.5,2.88) and (-3.5,3.17) .. (-4, 3.5) node[circle, fill=black, inner sep=1pt] at (-4,2.5) {};
               %
               \draw[->, ultra thick] (-1,0) -- (1,0);
               %
               \draw[thick] (4,0) circle (2.5cm);
               \draw[thick, blue] (1.5,0) .. controls (3.1, -0.5) and (4.8,-0.5) .. (6.5,0);
               \draw[thick, blue] (1.75,1.15) .. controls (3.23,0.65) and (4.77,0.65) .. (6.25,1.15);
               \draw[thick, blue] (2.5,2) .. controls (3.5, 1.8) and (4.5,1.8) .. (5.5,2);
               \draw[thick, blue] (1.75,-1.15) .. controls (3.23,-1.65) and (4.77,-1.65) .. (6.25,-1.15);
               \draw[thick, blue] (2.5,-2) .. controls (3.5, -2.3) and (4.5,-2.3) .. (5.5,-2);
               \draw[thick, blue] (4,2.5) .. controls (3.5,2.88) and (4.5,3.17) .. (4, 3.5) node[circle, fill=black, inner sep=1pt] at (4,2.5) {};
               \draw[thick, blue, rotate around={180:(4,0)}] (4,2.5) .. controls (3.5,2.88) and (4.5,3.17) .. (4, 3.5) node[circle, fill=black, inner sep=1pt] at (4,2.5) {};
   
   \end{tikzpicture} 
\end{document}