Graham's polygon haas maximal area, rather than perimeter! WFL On 1/9/09, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
Ron Graham was apparently the first solver for n=6
http://mathworld.wolfram.com/GrahamsBiggestLittleHexagon.html http://mathworld.wolfram.com/BiggestLittlePolygon.html http://www.davidson.edu/math/mossinghoff/
--Ed Pegg Jr
--- On Fri, 1/9/09, Andy Latto <andy.latto@pobox.com> wrote: From: Andy Latto <andy.latto@pobox.com> Subject: Re: [math-fun] Isodiametric problem To: "math-fun" <math-fun@mailman.xmission.com> Date: Friday, January 9, 2009, 1:15 PM
On Fri, Jan 9, 2009 at 1:35 PM, victor miller <victorsmiller@gmail.com> wrote:
A few days ago, at the AMS meeting, I saw a neat talk by Michael Mossinghoff about "isodiametic" problems -- e.g. Fix the diameter of a conv ex n-gon and ask for the ones with maximum perimeter.
If this is an interesting problem, and calculating the result for n <= 500 is a worthwhile feat, then my intuition that the answer is always a regular polygon must be wrong. What is the smallest n for which the answer is not regular, and what does the resulting n-gon look like?
My guess is that the answer is n = 5. If so, could this be related somehow to the fact that if you want to find the minimum x such that 5 discs of diameter x cover a disc of diameter 1, the configuration of these discs that exhibits the minimum is not a 5-fold symmetric one.
-- Andy.Latto@pobox.com
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