Imagine you have four towns, all spaced out in a square grid. What’s the most efficient way to link these towns with a motorway? You might guess anything from a circle, to again a square or two diagonals. Neither of these is the right answer. The problem involves determining the minimum path length required to link together a set of co-planar points, and is usually described in terms of a set of roads between a set of towns. As it turns out, find the minimum and optimum path between a set of towns is a pretty difficult problem to solve.
A brilliant fellow on YouTube shows an experimental solution to the motorway problem, using soap films, grids and surface tension. If you’re a teacher, use this guide to build your own soap film experiments.