We study all rotations of the unit sphere moving the starting point S with coordinates (1,0,0) to the point P. The axes of all such rotations happen to falls into the plane defined by the orange circle, bisecting SP.[br][br]Two of these rotations, the axes of which are shown by the red vectors [math]r_{1,}r_2[/math], are easy to see. Can you determine their angles of rotation?[br][br]Each rotation can be described by a quaternion. This applet defines [math]r_1,r_2[/math] in a purely geometric coordinate free way. There is a similar applet, where [math]r_1,r_2[/math] are calculated coordinate-wise and which gives an error if the x-coordinate of P is -1. That doesn't happen here.