The theory of the three dimensional rotation group has been pretty well studied and leads to some elegant interpretations of the parameters of the group. One of them uses arcs on the surface of a unit sphere, whereby the pole of the arc is the axis of rotation and the length of the arc is the angle of rotation. The arc can be positioned anywhere along its equator, but for the composition of rotations, the arcs should be placed tip to tail like vectors. The extreme points, together with the center of the sphere, define a new plane, and with it a new polar axis and arc of rotation. The curvature of the surface accounts for the noncommutativity of the composition.