As a taut rope of length l wound around a thin pole of radius r (r << l) is wrapped by a boy walking around the pole, each complete revolution consumes one circumference's worth of rope (2*pi*r) onto the pole, shortening the free (radial) length of rope by that amount. Since r is much smaller than l, the path is nearly a slow spiral where the radial distance from the pole is essentially the instantaneous free rope length, so the rate at which the boy approaches the pole equals the rate at which the free rope length decreases.