When our children were little, one of their favorite activities was playing with a train set. Much of the fun came from the act of assembling the pieces of wooden track, along with tunnels, bridges, switches, crossings, ramps, and other paraphernalia, into interesting arrangements. Our usual goal (I couldn’t resist the temptation to assist) was to create a layout that used every component that we had on hand.
A recent paper in Mathematics Magazine about train track layouts reminded me of these long-ago endeavors. It also neatly illustrated the power of mathematics in delineating a realm of possibilities. The paper showed track arrangements that my children and I had never thought to consider building.