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new definition of Kiepert axes?

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  • Steve Sigur
    Wilson, Fran├žois, Jean-Pierre, Bernard, Peter, and all, In checking Wilson s statements last night I noticed that there is a point on each axis of the Steiner
    Message 1 of 1 , Apr 1, 2006
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      Wilson, Fran├žois, Jean-Pierre, Bernard, Peter, and all,

      In checking Wilson's statements last night I noticed that there is a
      point on each axis of the Steiner ellipses where the its tripolar and
      its dual are perpendicular. The dual of course is always
      perpendicular to an axis, so at these points these lines are parallel
      to the Steiner axes. They seem to go through the Kiepert center mS
      (the medial Steiner point). Hence there seems to be a point on each
      axis whose dual and tripolar line form the axes of the Kiepert
      hyperbola. By intermediate values the points have to exist. That
      these lines are the Kiepert axes is conjecture.

      It will be easy to find these points but I am occupied by my conics
      writeups so it will wait. I suspect the the existence of the points
      is more interesting than the points themselves.

      Steve




      Triangle web page:
      http://paideiaschool.org/TeacherPages/Steve_Sigur/geometryIndex.htm

      Other math:
      http://paideiaschool.org/TeacherPages/Steve_Sigur/interesting2.htm
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