# What is the point of the Encyclopedia of Triangle Centers (aka, Kimberling centers)? [closed]

I recently stumbled across Kimberling's Encyclopedia of Triangle Centers database of points called Kimberling centers, which seem to be points defined relative to a triangle. Among them are some famous, relatively useful points, like the incenter and orthocenter.

But the database as of now has $$33,504$$ Kimberling centers defined. Many of them have no information on them except their definition and a large list of lines between other Kimberling centers on which they lay. Others don't even have that, and are just an arbitrary definition. I can't see how almost any of these could ever be useful; do they have any purposes that you know of?

• Wow. I had no idea. I'm confident it will be a gold mine to someone. It's a bit like OEIS for triangles. Maybe the book that ETC extends can shed light on the application of this.
– John
Commented Jul 3, 2019 at 19:56
• Well, a dictionary lists more words than any one person (besides a dictionary editor) will ever find useful, but, as a compilation, it's potentially useful to everyone. Each center listed has been of interest to someone; if someone else comes across the same center in their own research, it's convenient to have a place to check whether the discovery is novel. Also, keep in mind that we're looking at the ETC from the short end of its history; for all we know, the collinearity of $X(31415)$, the Lemoine Point, and the Nine-Point Center will be the key to warp propulsion 100 years from now.
– Blue
Commented Jul 3, 2019 at 21:14
• @John, one example I had fun with. Commented Jul 4, 2019 at 14:22

Honestly, I've never used nor read any definition of ETC points from $$20000$$ up but the biggest advantage of this encyclopedia is when you know how to construct some triangle centre (which you encountered trying to solve some geometry problem) and want to know something about its properties. Then the $$6$$, $$9$$, $$13$$ search that ETC provides really helps.