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2 inscribed parabola

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  • Steve Sigur
    Hello everyone, I only know of 2 cataloged inscribed parabolas: the Kiepert and Yff parabolas with perspectors :1/(cc-aa): and : 1/(c-a) :. The affine methods
    Message 1 of 1 , Oct 1, 2006
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      Hello everyone,

      I only know of 2 cataloged inscribed parabolas: the Kiepert and Yff
      parabolas with perspectors :1/(cc-aa): and : 1/(c-a) :.

      The affine methods I have been creating show that each inparabola can
      be associated with a line through G. The Kiepert parabola is
      associated with GK and the original Yff parabola (there are actually
      four of them) with GIo, where Io is the original incenter.

      (Details of this can be found on my web pages, linked below. Check
      out the section on lines though G in the document on conic types. )

      The Jerabek hyperbola leads to two interesting inparabolae.

      Note: the "switched" conic has center and perspector interchanged.

      The line from G through J, the Jerabek center leads to the inparabola
      with
      perspector: intersection of the Jerabek hyperbola and the Steiner
      ellipse
      Focus: the T, the Tarry point.
      Axis: through T parallel to HD, where D = tH, the isotomic of H.
      Directrix: H U, where U is the 4th intersection of the switched
      Jerabek hyperbola with the Steiner ellipse.

      The other comes from the line between G and the Jerabek perspector.
      perspector: U, the intersection of the switched Jerabek hyperbola
      and the Steiner ellipse
      Focus: the "pro" of this point
      Axis: through focus parallel to ~J, where J is the Jerabek center.
      Directrix: HT

      Steve

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

      The arml website is now officially on line. Find it here.

      The Secrets of Georgia ARML 1
      Find it here.

      The Secrets of Georgia ARML 3 website, is at
      http://stuff.mit.edu/~borisa/georgia-arml
      Username: arml
      Password: soga3

      http://www.mandelbroit.org





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