structure of ETC

ETC is such a valuable resource but Many of its points seem not very relevant. Since I am plotting all the points of ETC I want to make one that is not filled with points of little relevance. My guess is that about a third of ETC are such points.

A point of little relevance is one that in not on any lines, is not the center of conics, is not on conics, is not related to other points by any of the 20+ operations that Kimberling uses. It takes talent to be so unconnected. So if a point cannot manage to have any of so many properties, I plan to drop it from the pictures I make.

155-161     of various strong triangles (tangential, orthic)

298-350      isotomic conjugates

447 - 457    Hirst inverse   or Euler substitution points           not very important -- the Euler substitution points are irrelevant (except perhaps as Euler subst pts)

463--475   Euler intercepts of various lines or cross conjugates

 Centers 503- 510,  

173, 174, 258, and 351- 364 are associated with isoscelizers.       The isoscelizer concept is important but most of these points are not

Centers 511- 526,  

30, and others, lie on the line at infinity. 

Thus, a collection of collinearities reported for each of these centers comprises a family of parallel lines. 

527 - 545  directions of vectors   more points at infinity

555-559    Answers to "question A", an interesting question, but most of these points are algebraically isolated from the rest of ETC.

 Centers 566 - 584     are on the Brocard axis

648 - 691    trilinear poles and cross differences

696-727      even(n,m) curve pts        of minor or no relevance

more are coninued to 761 with somewhat more relevance.

776-797   more odd(....) pts, almost all irrelevant

802-819  more of the same, many irrelevant.

822-839  more of same mostly relevant this time.

stopped at 1000

1512 - 1568   orthojoin of individual points         an irrelevant section

I plan to make a new picture of the centers listed in ETC.

I learned these things from the first round of pictures done by Nikolaos and me.

Infinite points may not plot well, they must be removed. Peter and Nikolaos  have listed these.

The Brisse compilation in Barycentrics did not include 2 fold (fissile) points; they must be added. I think Nikolaos does include them.

The circumcircle and Euler line are abnormally represented. For example there is a section of ETC where the intersections of many lines with the Euler line are compiled. This is fine but has not been done for any other line such as the Brocard line.

The Steiner ellipse is as important as the circumcircle, but there are amost no points listed in ETC on it. Ab initio, one would think that the Steiner ellipse, the line at infinity, and the circumcircle  

would have an equal number of points.

Many points in ETC are irrelevant and are just noise. I plan to drop these groups of points.

The orthojoin points  1512 - 1568

most points with definitions like the following

X(777) = o-(- 4, 1) CIRCUMCIRCLE POINT

Trilinears  = 1/[a -5(b1 - c1) + a0(b -4 - c -4)]

X(777) lies on the circumcircle.

----

most points associated with isoscelizers

I will soon present an extension of this list of points I plan to drop.