[math-fun] Extension of a theorem on n-gons
Steve Gray posted the message below. It was intercepted (too big), and Steve has offered to send the PDF of his paper to interested parties. His address is "Steve Gray" <stevebg@adelphia.net> The paper is about placing similar figures on the edges of a polygon, such as the construction of equilateral triangles on the edges of a starting triangle. Rich rcs@cs.arizona.edu ---------------------- 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.
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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participants (2)
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Eugene Salamin -
Richard Schroeppel