Which Way Did You Say That Bicycle Went?
David L. Finn · Mathematics Magazine · 2004
In this paper, we provide a method for constructing such ambiguous tire tracks, where one cannot determine from the shape of the tracks which direction the bicycle was traveling. The pair of tracks in FIGURE 1 is in fact an example of such a pair of ambiguous tracks. Our method to produce these involves only a slight variation of the solution method for the original problem [8]. Our method for constructing ambiguous tire tracks starts with the construction of a special initial back-tire track segment. From this initial back-tire track segment, we can construct a front-tire track segment (which will be longer) by pushing the bicycle forward in both possible directions of motion along the back-tire track. The next step is to extend the back-tire track by pushing the bicycle backwards along the newly created front-tire track in both possible directions. This physical construction can be continued iteratively until either the front-tire track or the back-tire track develops a singularity. To see a demonstration of this mathematical construction, the interested reader can view animations at the author's website [5].