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

Re: [EMHL] Wernau point (Fermat concurrences)

Expand Messages
  • Darij Grinberg
    Dear Jean-Pierre Ehrmann, LOTS OF THANKS FOR THE BARYCENTRICS !! I have tested them in the 6-9-13 case, they are correct. The search number (in actual
    Message 1 of 10 , Apr 6 3:26 AM
    View Source
    • 0 Attachment
      Dear Jean-Pierre Ehrmann,

      LOTS OF THANKS FOR THE BARYCENTRICS !!

      I have tested them in the 6-9-13 case, they are correct. The search
      number (in actual TRILINEARS) is then

      1st Wernau point -13.209317003851505465.

      I call the point W the 1st Wernau point, since an analogous 2nd
      Wernau point can be found with equilateral triangles constructed
      inwards. Also, two Wernau-Napoleon points can be found for Napoleon
      triangles instead of Fermat triangles, as Floor van Lamoen has
      noticed.

      In order to get the 2nd Wernau point, we must undertake fissile
      extraversion. We then get the barycentrics

      x = a^2(x1 - 2d x2/root(3)), etc.

      and the search number (in actual TRILINEARS)

      2nd Wernau point -6.9391333766227036231.

      Sincerely,
      Darij Grinberg
    • Floor en Lyanne van Lamoen
      Dear Darij and Jean-Pierre, I just found the same barycentrics as did Jean-Pierre. The centers of the three circles form a triangle perspective to ABC through
      Message 2 of 10 , Apr 6 5:05 AM
      View Source
      • 0 Attachment
        Dear Darij and Jean-Pierre,

        I just found the same barycentrics as did Jean-Pierre.

        The centers of the three circles form a triangle perspective to ABC
        through X_61 (X_62).

        Kind regards,
        Sincerely,
        Floor.

        Darij Grinberg wrote:
        >
        > Dear Jean-Pierre Ehrmann,
        >
        > LOTS OF THANKS FOR THE BARYCENTRICS !!
        >
        > I have tested them in the 6-9-13 case, they are correct. The search
        > number (in actual TRILINEARS) is then
        >
        > 1st Wernau point -13.209317003851505465.
        >
        > I call the point W the 1st Wernau point, since an analogous 2nd
        > Wernau point can be found with equilateral triangles constructed
        > inwards. Also, two Wernau-Napoleon points can be found for Napoleon
        > triangles instead of Fermat triangles, as Floor van Lamoen has
        > noticed.
        >
        > In order to get the 2nd Wernau point, we must undertake fissile
        > extraversion. We then get the barycentrics
        >
        > x = a^2(x1 - 2d x2/root(3)), etc.
        >
        > and the search number (in actual TRILINEARS)
        >
        > 2nd Wernau point -6.9391333766227036231.
        >
        > Sincerely,
        > Darij Grinberg
      Your message has been successfully submitted and would be delivered to recipients shortly.