From: utzoo!decvax!ucbvax!CAD:tektronix!tekecs!steveb Newsgroups: net.physics Title: A Mathematical Question Article-I.D.: tekecs.612 Posted: Fri Mar 11 13:32:14 1983 Received: Sun Mar 13 05:39:58 1983 Ever hear a claim like "Podunk County has more miles of beaches than the Atlantic Ocean"? This leads me to ask: Take a perfectly circular lake with diameter 1 / pi and thus a circumference (shoreline) of 1. Now deform the shoreline by filling in parts of the lake (i.e. the new lake may have any shape whatsoever as long as it lies entirely within the boundaries of the old lake). What is the maximum shoreline you could obtain in this way? Can an algorithm be specified that tells one how to deform the original so as to get to the maximal? What is its shape? It seems to me that posting responses to the net is appropriate, but if you wish to mail me something probably not of general interest, I am: ucbvax!teklabs!tekecs!steveb or decvax!tektronix!tekecs!steveb (DONT use header address)