From: brock@ccr-p.ida.org (Bradley Brock)
Newsgroups: sci.math
Subject: Re: Morgan's Conjecture
Date: 18 Jan 1995 09:14:47 -0500

In article <D1zLEo.3Ev1@austin.ibm.com> , fossum@austin.ibm.com writes:
>  If you take any triangle and trisect each side, and connect the trisection
>  points with the opposite vertices, you get six lines within the triangle 
>  which delineate a hexagon in the center.  The are of the hexagon is exactly
>  1/10th the area of the original triangle.  This was previously known.
>  The new proposition is that if you divide the sides of the triangle into
>  any odd number of equal segments, the resulting (smaller) hexagon in the
>  center compares, in area, to the original triangle by some ratio which is
>  a relatively simple function of the odd number of segments each side is 
>  divided into.
>
>This amused me when I read it in the newspaper, and I have derived (I think)
>the function in question.  I would like to speak with Morgan or his mentor, 
>to verify my suspicions.

Look in the newsgroup geometry.pre-college under
Subject: Marion's theorem
From: DavidJ4862
who states the answer is 1/8(3n+1)(3n-1)
and
From: John Conway
who sketches a proof.
-- 
(c) Copyright 1994 Bradley Brock, IDA/CCR-P, Thanet Road, Princeton, NJ  08540
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