Date: Sat, 27 Jul 1996 23:33:04 -0500 (CDT) From: [Permission pending] To: rusin@math.niu.edu Subject: Re: morley and all that [deletia -- djr] Proofs of Morley's theorem aren't difficult to locate, for the few folks who still use mathematics libraries instead of asking others for help. Many "college geometry" texts give proofs, including Coxeter. I don't recall whether it is proved by R. Johnson or N. A. Court, but the odds are very good that a clean, clear argument is given by at least one, if not by both. I once heard a seminar talk given by J. W. Peters, perhaps 20 years ago, in which he explain the context of Morley's theorem and showed how Morley came upon it. My memory of the details is completely gone, but I recall that there is much more interesting geometry nearby. There is a well studied way of doing elementary analytic geometry using complex notation and language (ultimately based on the fact that 2x = z + z* and 2y = z - z* (writing * for the complex conjugate). In this notation there are ways of handling lines, slopes, circles, etc., and in particular the notion of slope has a meaningful complex extension. Morley's result pops out of a perfectly natural question in this context. If you are interested, I'll try to ferret out a reference-- I seem to remember an expository article somewhere, perhaps in the Monthly or Elemente der Mathematik, sometime in the last 30 years--but it may take me a while to locate it because I do not recall either the title or the author or the journal for sure. [deletia -- djr] ============================================================================== [I did find this article in MathSciNet: -- djr] Mathematical Reviews on the Web 3,251e 48.0X Peters, J. W. The theorem of Morley. Nat. Mat. Mag. 16, (1941). 119--126. © Copyright American Mathematical Society 1942, 1998