Suppose you have a finite set of points in the plane. The process known as "convex peeling" arose as one way of defining the "median" of a finite set of 2-dimensional data, analogous to the usual one for 1-dimensional data: Let the set of points be X. Define X_0 = X and X_(n+1) = X_n - {p in X_n | p is on the boundary of the convex hull of X_n} for n >= 0. This sequential "filtration" of X is known as convex peeling. About 37 year ago someone showed me that if you start with a large number of points uniformly distributed in a square and then proceed to remove them in stages via "convex peeling" — the boundaries of the last groups of points remaining are exceedingly circular. So that there appears to be a true statement, something like: ----- With probability = 1, the shape of the normalized result of convex peeling [toward the end of the process] approaches [in some sense] a circle, as the number of points approaches oo. ----- But I've never seen a proof of this. Any ideas? —Dan