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Re: Isotomy and Isogonality

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  • Jeff
    Dear friends, Relax the definition of point and consider the vertices of our triangle as being elements (skewed circulants for example.) Can we then define the
    Message 1 of 16 , Jun 1, 2007
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      Dear friends,

      Relax the definition of point and consider the vertices of our triangle
      as being elements (skewed circulants for example.) Can we then define
      the isotomic and isogonal conjugate and still maintain their "natural"
      properties?

      Sincerely, Jeff
    • Jeff
      Dear Nikos I m looking for an isomorphism here. Best Regards, Jeff [ND]
      Message 2 of 16 , Jun 2, 2007
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        Dear Nikos

        I'm looking for an isomorphism here.

        Best Regards, Jeff


        [ND]
        > The word isosceles comes from ancient Greek
        > Mathematicians and means
        > iso = equal
        > scelos-sceli = legs.
        >
        > So I conjecture that somebody?? used Greek words.
        > If AP and AP' are isogonal conjugate lines wrt ABC
        > then angle BAP = angle P'AC and
        > isogonal = equal angle in Greek.
        >
        > If X, X' are on BC and AX and AX' are isotomic
        > conjugate then they cut on BC equal segments
        > BX = X'C
        > and isotomic = equal cutting in Greek.
      • Jeff
        Dear Francois, I thought maybe by complexification you meant a complicated number like that defined in [1] below. ... Sincerely, Jeff [1] I.J. Good, A
        Message 3 of 16 , Jun 10, 2007
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          Dear Francois,

          I thought maybe by "complexification" you meant a 'complicated number'
          like that defined in [1] below.

          > Now in the contrary, why this is true with the pair (I, J) of the
          > circular points is another matter dealing with the complexification
          > of the plane.

          Sincerely, Jeff

          [1] I.J. Good, "A simple generalization of analytic function theory",
          Expositiones Mathematicae, Expo. Math 6 (1988), 289-311, Published by
          Bibliographisches Institut & F.A. Brockhaus AG 1988.
        • Jeff
          Dear Bernard, ... If we use X2 and X6 as the real foci of the inconic, then what or where are the imaginary ones? Sincerely, Jeff
          Message 4 of 16 , Jun 20, 2007
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            Dear Bernard,

            > I think it's just the same as foci of inconics : two points are real
            > and two are imaginary.
            >
            > take a look at :
            >
            > http://perso.orange.fr/bernard.gibert/Classes/cl031.html


            If we use X2 and X6 as the real foci of the inconic, then what or where
            are the imaginary ones?

            Sincerely, Jeff
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