Could you provide a statement of the 100 year old result, and of your extention to it?
Steve Gray> Some of you may be interested in a paper of mine in the March 2003 American Mathematical Monthly, which arrived by mail here today. It's a significant extension of a result that's almost 100 years old, one that has been described as "remarkable" and "beautiful." I enclose a PDF file of the paper in its final format. This is the first of a planned series of papers on further generalizations of this theorem in plane geometry. These theorems apply to n-gons, where n > 2. Proofs are done with elementary matrix theory. For the most part, the results are harder to find than to prove, and while I have two or three more generalizations established and proved, I have been working to characterize and delimit the parameters for two other conjectures for at least six months. I didn't think there was that much left in "ordinary Euclidean" geometry.
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