- 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]> 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.

> Now in the contrary, why this is true with the pair (I, J) of the

Sincerely, Jeff

> circular points is another matter dealing with the complexification

> of the plane.

[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. - Dear Bernard,

> I think it's just the same as foci of inconics : two points are real

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

> and two are imaginary.

>

> take a look at :

>

> http://perso.orange.fr/bernard.gibert/Classes/cl031.html

are the imaginary ones?

Sincerely, Jeff