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. -- (c) Copyright 1994 Bradley Brock, IDA/CCR-P, Thanet Road, Princeton, NJ 08540 brock@ccr-p.ida.org,brock@alumni.caltech.edu,609-279-6350(w),609-924-3061(fax) "Football exemplifies the worst features of American life: it's violence punctuated by committee meetings."--George Will