An amateur astronomer was staring into the dark, shiny night sky. Far away from usual hustle-bustle of the city and its pollution clouded sky, he was trying to locate some stars on his sophisticated telescope. He had a list of stars and some numbers scribbled onto a sheet of paper. Against each star, he had written two values- an azimuth angle and an angle of elevation or altitude. To direct to a point in a 3D space, after all, two ‘rotation’ values should suffice. You first indicate the azimuth angle (angle swept on a horizontal reference plane starting from a reference line on it). Then the elevation angle tells how high above this horizontal plane you ‘lift’. <br \>

Now if he were to locate an airplane instead (it is quite unlikely that he would find one in that desolate paradise of his!) he would require another ‘rotation’ value to specify its orientation. Think of it, just pointing to the airplane as if it were a star will not tell the direction it is travelling in. That validates the necessity for a third parameter. The lesson learnt from the story is this- for completely specifying the orientation of an ‘extended object’ like the airplane with respect to a reference frame, three rotation parameters are a minimum. <br \>