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Re: [EMHL] Inscribed Rectangles

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  • Bernard Gibert
    Dear Paul and Antreas, ... [PY] ... I had computed this locus too and left it aside since this cubic does not seem to be of much interest. All I can say is it
    Message 1 of 10 , Aug 5, 2001
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      Dear Paul and Antreas,
      >
      [PY]
      > cyclic sum aa(v-w)/(SC.v-SB.w) = 1.
      >
      > Now, Bernard, what kind of cubic is this?
      >
      I had computed this locus too and left it aside since this cubic does not
      seem to be of much interest.
      All I can say is it has a singularity at X69=isotomic of H with two
      rectangular tangents at this point.
      It is not an isocubic.

      The six common points with Jerabek hyperbola are A,B,C,X69 (double) and the
      isotomic conjugate of X631.

      We could try to go back to Lemaire's construction of cubics with a double
      point (I posted something on that last year)

      Best regards

      Bernard
    • Bernard Gibert
      Dear Paul and Antreas, I want to correct a stupid confusion I made in my previous message : ... The sixth point is not the isotomic conjugate of X631 but the
      Message 2 of 10 , Aug 5, 2001
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        Dear Paul and Antreas,

        I want to correct a stupid confusion I made in my previous message :
        I wrote :
        > The six common points with Jerabek hyperbola are A,B,C,X69 (double) and the
        > isotomic conjugate of X631.

        The sixth point is not the isotomic conjugate of X631 but the isogonal
        conjugate of [a^2(b^4 + c^4 - a^4 -6b^2c^2) ; ... ; ... ] which is on the
        Euler line and unknown in ETC.

        Sorry about that !

        Best regards

        Bernard
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