There is a semi-circular drive on the west side of the campus, and I usually bike or walk up it on my way in to school every day. Most pedestrians walk on the sidewalk on the outer edge. Let r denote the radius to the sidewalk on the inner edge of the drive, and r’ the width of the road. Then a pedestrian on the outer edge walks a distance of (π/2) r + r’ to reach the east side of the top of the drive, whereas a pedestrian on the inner edge walks a distance of (π/2) (r + r’). Clearly the inner path is shorter, yet fewer people take it.
As an extra credit problem, why does it make sense for me to take the outer path anyway?