Re: [math-fun] Puzzle to find a function D^2 -> [0,1]

Quoting Dan Asimov <dasimov@earthlink.net>:

on a theorem of Cauchy:

Theorem: Given two convex curves A,B in the plane with B lying inside A, then length(B) < length(A).

Is it fair to give this one to Cauchy? Archimedes must have assumed something like it to estimate the circumference of a circle as being between the in- & circumscribed polygons. Was Cauchy just bringing the rigor up to modern standards, or is some non-obvious insight required? Rich