--- In

Hyacinthos@yahoogroups.com, "jpehrmfr" <Jean-

Pierre.Ehrmann.70@...> wrote:

>

> Dear Floor and Hauke

> [FvL]

> > Your suggestion about the Neuberg cubic is interesting, but not

> correct I

> > think. How does the circumcenter fit in this???

> And what about the incenter or X(399)?

No trick questions please, *you* are the math buffs :-)

Trying to weasel me out of this one. As I said, the

Neuberg cubic may be written as symmetric function

of a flock of tangents. It can happen that the function

factors to hell for certain special points D.

Another formulation: Like the circle, the Neuberg cubic

is defined by 3 points. An ellipse with eccentricity

e=0.5 is defined by 4 points. Let the 4 points lie on

a square. Oopsie! 2 solutions!

Thus: *Almost* every point on the Neuberg cubic has the QP,

#1 and #3 are "too special", of #399 I frankly don't know

and the computation is rather lengthy. But when Darij

said so... :-)

Hauke