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Which Cubic is this??

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  • Antreas Hatzipolakis
    -a^2 b^2 c^4 x^3 y - b^4 c^4 x^3 y + b^2 c^6 x^3 y + a^4 c^4 x y^3 + a^2 b^2 c^4 x y^3 - a^2 c^6 x y^3 + a^2 b^4 c^2 x^3 z - b^6 c^2 x^3 z + b^4 c^4 x^3 z +
    Message 1 of 3 , Dec 3, 2011
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      -a^2 b^2 c^4 x^3 y - b^4 c^4 x^3 y + b^2 c^6 x^3 y + a^4 c^4 x y^3 +
      a^2 b^2 c^4 x y^3 - a^2 c^6 x y^3 + a^2 b^4 c^2 x^3 z -
      b^6 c^2 x^3 z + b^4 c^4 x^3 z + a^6 c^2 y^3 z - a^4 b^2 c^2 y^3 z -
      a^4 c^4 y^3 z - a^4 b^4 x z^3 + a^2 b^6 x z^3 - a^2 b^4 c^2 x z^3 -
      a^6 b^2 y z^3 + a^4 b^4 y z^3 + a^4 b^2 c^2 y z^3

      See the locus problem HERE:

      http://anthrakitis.blogspot.com/2011/12/nice-if-true.html

      APH


      [Non-text portions of this message have been removed]
    • Bernard Gibert
      Dear Antreas, this is the Euler-Morley quartic Q002. http://bernard.gibert.pagesperso-orange.fr/curves/q002.html Best regards Bernard ... [Non-text portions of
      Message 2 of 3 , Dec 3, 2011
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        Dear Antreas,

        this is the Euler-Morley quartic Q002.

        http://bernard.gibert.pagesperso-orange.fr/curves/q002.html

        Best regards

        Bernard

        > -a^2 b^2 c^4 x^3 y - b^4 c^4 x^3 y + b^2 c^6 x^3 y + a^4 c^4 x y^3 +
        > a^2 b^2 c^4 x y^3 - a^2 c^6 x y^3 + a^2 b^4 c^2 x^3 z -
        > b^6 c^2 x^3 z + b^4 c^4 x^3 z + a^6 c^2 y^3 z - a^4 b^2 c^2 y^3 z -
        > a^4 c^4 y^3 z - a^4 b^4 x z^3 + a^2 b^6 x z^3 - a^2 b^4 c^2 x z^3 -
        > a^6 b^2 y z^3 + a^4 b^4 y z^3 + a^4 b^2 c^2 y z^3
        >
        > See the locus problem HERE:
        >
        > http://anthrakitis.blogspot.com/2011/12/nice-if-true.html
        >
        > APH



        [Non-text portions of this message have been removed]
      • Antreas Hatzipolakis
        Dear Bernard Thank you. The email correspondace between Francisco and me took place after midnight, and it seems we were semi-sleeping :-) Antreas ...
        Message 3 of 3 , Dec 4, 2011
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          Dear Bernard

          Thank you.

          The email correspondace between Francisco and me took place
          after midnight, and it seems we were semi-sleeping :-)

          Antreas


          On Sun, Dec 4, 2011 at 6:16 AM, Bernard Gibert <bg42@...> wrote:

          > **
          >
          >
          > Dear Antreas,
          >
          > this is the Euler-Morley quartic Q002.
          >
          > http://bernard.gibert.pagesperso-orange.fr/curves/q002.html
          >
          > Best regards
          >
          > Bernard
          >
          >
          > > -a^2 b^2 c^4 x^3 y - b^4 c^4 x^3 y + b^2 c^6 x^3 y + a^4 c^4 x y^3 +
          > > a^2 b^2 c^4 x y^3 - a^2 c^6 x y^3 + a^2 b^4 c^2 x^3 z -
          > > b^6 c^2 x^3 z + b^4 c^4 x^3 z + a^6 c^2 y^3 z - a^4 b^2 c^2 y^3 z -
          > > a^4 c^4 y^3 z - a^4 b^4 x z^3 + a^2 b^6 x z^3 - a^2 b^4 c^2 x z^3 -
          > > a^6 b^2 y z^3 + a^4 b^4 y z^3 + a^4 b^2 c^2 y z^3
          > >
          > > See the locus problem HERE:
          > >
          > > http://anthrakitis.blogspot.com/2011/12/nice-if-true.html
          > >
          > > APH
          >
          >
          >


          [Non-text portions of this message have been removed]
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