Wednesday, October 03, 2007

October 2007: On the right track

Your young cousin has made an elaborate train track for his toy trains. He used track pieces of two varieties--ones that are straight and ones that are arcs of a circle. The gauge of the track (the distance between the rails) is 1". Suppose he drives his train around the track one time counterclockwise. How much farther did the right wheels travel than the left wheels? (You may assume that the track is convex, but in fact, you don't need this assumption--you just need there to be no crossovers.)