Re: Isotomy and Isogonality

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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
Message 1 of 16 , Jun 1 1:43 AM
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
• Dear Nikos I m looking for an isomorphism here. Best Regards, Jeff [ND]
Message 2 of 16 , Jun 2 9:13 PM
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.
• 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 6:39 PM
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",
Bibliographisches Institut & F.A. Brockhaus AG 1988.
• 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 4:28 AM
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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