latex-pictures

 % This picture represents the fact that geodesics locally minimize distances
 % Copyright Pablo (C) 2021
 \begin{tikzpicture}[scale=0.5]
   % The cirference
   \draw (0, 0) circle (3);
 
   % The equator
   \begin{scope}
     \clip (-3, 0) rectangle (3, -3);
     \draw ellipse (3 and 1);
   \end{scope}
 
   % Greenwhich
   \begin{scope}
     \clip (-3, -3) rectangle (0, 3);
     \draw ellipse (1 and 3);
   \end{scope}
 
   % The curve
   \begin{scope}
     \clip (-3, 0) rectangle (0, -3);
     \draw[very thick] ellipse (1 and 3);
   \end{scope}
   \begin{scope}
     \clip (3, -3) rectangle (0, 3);
     \draw[very thick, dotted] ellipse (1 and 3);
   \end{scope}
 
   % The ends
   \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt);
 
   \draw (-0.87, -1.5) circle (0.3);
   \draw (-1.17, -1.5) -- (-4, 1);
 
   % Zoom in ares
   \begin{scope}[shift={(-6, 1)}]
     \draw (0, 0) circle (2);
 
     % The geodesic
     \draw[very thick] (0, -2) -- (0, 2);
     \filldraw (0, -2) circle (2pt) (0, 2) circle (2pt);
 
     % Another curve
     \draw[dotted] (   0,    2) to[out=180, in=90] 
                   (-0.6,  1.4) to[out=270, in=150] 
                   ( 0.5,  0.7) to[out=-30, in=0] 
                   ( 0.3,  0.1) to[out=180, in=180] 
                   ( 0.5,  0.6) to[out=0, in=120] 
                   ( 1.3,  0.7) to[out=-60, in=60] 
                   ( 0.4, -0.5) to[out=240, in=90] 
                   (   0,   -2);
   \end{scope}
 \end{tikzpicture}