Wikipedia http://en.wikipedia.org/wiki/Gibbs_phenomenon probably does not have a very good discussion. But anyhow, they claim the heights of the Gibbs phenomenon peaks asymptotically are given by (for the Nth peak; note N=even yields "reverse peaks" below 1, N=odd yields "normal peaks" above 1) integral from -infinity to N sin(pi*x)/(pi*x) dx If so, then I agree: the height differences between successive peaks clearly behave eventually proportionally to 1/N for the Nth peak. Hence the Fourier reconstruction of the unit step function will in the limit (where we get pointwise convergence to that step function at any fixed x>0 or any fixed x<0, hence the Gibbs peaks all horizontally move closer together) indeed will have arc-length tending to infinity over any fixed finite segment of the x-axis containing 0 inside it. -- Warren D. Smith http://RangeVoting.org