latex-pictures

diff --git a/quaternion-rotation.tikz b/quaternion-rotation.tikz
@@ -1,15 +1,17 @@
-% This drawing represents the correspondance between conjugation by unitary
-% quaternions and rotations in the 3-dimensional euclidian space
+% This drawing represents the correspondance between conjugation by pure
+% unitary quaternions and rotations in the 3-dimensional euclidian space: the
+% coordinates of a unitary quaternion p number with zero real cofficient induce
+% a line through the origin in the 3-dimensional enclidian space, and
+% conjugation by cos t + p sin t acts as rotation by 2 t around this axis.
 % Copyright Pablo (C) 2021
 \begin{tikzpicture}
   % The rotation axis
   \begin{scope}[rotate=-60]
     % The axis
-    \draw[->] (0, 0) -- (0, 2.5) node[right]{$\mathrm{Im}\,q$};
+    \draw[->] (0, 0) -- (0, 2.5) node[right]{$p$};
 
     % The rotation
-    \draw[->] (0.43, 2) node[right]{$\theta=\frac{\arccos(\mathrm{Re}\,q)}{2}$}
-                        arc (30:360:0.5 and 0.25);
+    \draw[->] (0.43, 2) node[right]{$2 \theta$} arc (30:360:0.5 and 0.25);
 
     % The origin and the intersection of ratation axis with the unit sphere
     \filldraw (0, 0) circle (1pt) (0, 1) circle (1pt);