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 , 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.
--
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