Constructing a Map from a Table of Intercity Distances

Abstract

Since the array is symmetric, we have displayed only the lower triangle. The main diagonal consists of zeroes. If this is the only information we have available, is it possible for us to reconstruct the map? To be more precise, can we position the cities in the plane so that the intercity distances correspond to those in the chart? We give a partial solution to this question. It is easy to see that any solution we obtain is not unique since the distance between points is invariant under translation,