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

15393Re: [EMHL] Re: Cevian Trace Equal Area Points

Expand Messages
  • Francois Rideau
    Aug 1, 2007
      Dear Nikos and Tuan
      Thanks for your interesting remarks.
      Of course in choo-choo theory, these lines La, Lb, Lc play a central role
      and I have called them equal area axis.
      Notice that their construction is affine! I had also my own construction
      slightly different from yours.
      As for Tuan formula, I would be happy to have a name if any for the dual
      point M(q*w - r*v::)of the line through P(p:q:r) and Q(u:v:w) given by their
      barycentrics.
      Friendly
      Francois
      PS As Nikos notice, point isotomic of the areal center also plays an
      important role in choo-choo theory.
      As I go away from Paris in Britanny for several weeks even months far away
      from the web, I give you a choo-choo configuration, so you can think about
      me in this summer time:
      Instead of cevian tiangles, I will look at pedal triangles PaPbPc and QaQbQc
      of points P and Q wrt triangle ABC and I call L the line through P and Q.
      Let E be the equicenter and S the areal center of the pedal triangles.
      Then:
      1° E is the orthopole of line L wrt ABC.
      2° S is on the ABC-circumcircle and its Simson line is parallel to line L.

      The first point was knew by Neuberg for a very very long time and maybe
      that's why he found the orthopole. The first proof I saw was due to
      V.Thebault
      As for the second point, I would be happy to have some reference if any.
      Of course these properties of points E and S are shared by any pair of
      triangles of points on line L but this is another (choo-choo) story.


      [Non-text portions of this message have been removed]
    • Show all 18 messages in this topic