Mathematical description of movement vs practical interpretations or why some apparently pertinent questions have no meaningful answers

This publication is motivated by our early contacts with medical specialists, when we - as IT researches - were often asked to resolve, by purely mathematical means, questions which went beyond the possibilities offered by geometry. The mathematical description of rigid body motion will be explained, along with the limits of information which can be extracted from it. In particular, if the movement is given by an initial and final position only, it can be decomposed into translation and rotation in an infinity of ways which are obviously different, although equivalent in terms of final result, and none of them can be rejected without additional information about the underlying kinetic setup.