Loading ...
Sorry, an error occurred while loading the content.

22026Fwd: [EGML] 3 LSD points concerning a hexagon in a triangle

Expand Messages
  • Antreas Hatzipolakis
    Dec 10, 2013
    • 0 Attachment


      ---------- Forwarded message ----------
      From: Seiichi Kirikami <seiichikirikami@...>
      Date: Tue, Dec 10, 2013 at 11:47 AM
      Subject: [EGML] 3 LSD points concerning a hexagon in a triangle
      To: Anopolis@yahoogroups.com


       

      Dear friends,
       
      Given a triangle ABC and a point P, we denote by Ba and Ca the intersections of the line through P parallel to BC with AB and AC respectively. Cb and Ab, Ac and Bc are defined cyclically. We consider 3 LSD points concerning the hexagon AcAbBaBcCbCa, where LSD means the least square distances.
       
      (1) If the square sum of the sidelengths of the hexagon (AcAb)^2+(AbBa)^2+(BaBc)^2+(BcCb)^2+(CbCa)^2+(CaAc)^2 is minimal, the barycentrics of P={5a^4+16a^2(b^2+c^2)+3(b^2+c^2)^2; ; }. kx=2.1112325135.. (non ETC).
       
      (2) If the square sum of the diagonals of the hexagon (AbCb)^2+(BcAc)^2+(CaBa)^2 is minimal, P=X(194).
       
      (3) If the square sum of the sidelengths of 2 triangles (AbBc)^2+(BcCa)^2+(CaAb)^2+(AcBa)^2+(BaCb)^2+(CbAc)^2 is minimal, P=X(6).
       
      Best regards,
      Seiichi.

      _