Of the many factors affecting the collision problem, the mathematics of relative motion is the one most susceptible to formal analysis. Moreover, this ‘collision geometry’ must form the basis of any investigation into the instrumental, operational and human factors involved. It is therefore surprising that no complete description of the (mathematically) simple relationships is readily available. The object of this paper is to present such a connected account of the mathematics of relative motion, in so far as it appears relevant to the collision problem and within the limitations of time and space available.