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22028Fwd: [EGML] X(5390) refined

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  • Antreas Hatzipolakis
    Dec 16, 2013
    • 0 Attachment


      ---------- Forwarded message ----------
      From: Chris van Tienhoven
      Date: Mon, Dec 16, 2013 at 1:05 PM
      Subject: [EGML] X(5390) refined
      To: Anopolis@yahoogroups.com


      Dear friends,

      While working on a Morley-related problem, I again stumbled on X(5390).
      I simplified the expression of the barycentric coordinates of this point several times.
      At first I found a solution of many pages, then many rules, then about 30 terms.
      The most recent simplification was a solution of 8 terms.
      Now I simplified it to 4 terms.
      The 1st trilinear coordinate of X(5390) is:
      - Sin[B] Sin[C]
      + Sin[A] Cos[(2 A)/3 - Pi/6]
      + Sin[B] Cos[A + B/3 + Pi/6]
      + Sin[C] Cos[A + C/3 + Pi/6]

      Working with Trigonometric formulas isn't that easy.
      Even now I cannot assure that this is the most simple solution.

      Best regards,

      Chris van Tienhoven