  Recently Andrews and Bryan [3] discovered a comparison function which allows
them to shorten the classical proof of the well-known fact that the curve
shortening flow shrinks embedded closed curves in the plane to a round point.
Using this comparison function they estimate the length of any chord from below
in terms of the arc length between its endpoints and elapsed time. They apply
this estimate to short segments and deduce directly that the maximum curvature
decays exponentially to the curvature of a circle with the same length. We
consider the expansion of convex curves under inverse (mean) curvature flow and
show that the above comparison function also works in this case to obtain a new
proof of the fact that the flow exists for all times and becomes round in
shape, i.e. converges smoothly to the unit circle after an appropriate
rescaling.
