triangle centers

[eub]

1. incenter
2. centroid
3. circumcenter
4. orthocenter
my education in compass-and-straightedge construction ended here
5. nine-point center
A dude has a list of several thousand more, like they were integer sequences or something.

The coolest part is the theory of what a triangle center is.

Mathworld scatterplots them:

Comments

[randomdreams.livejournal.com]

I had never even considered that, and now my brain is broken into pieces.

[bhudson.livejournal.com]

I will have to show this to the people at work who say "the geometric center" as if that was well defined.

By the way, another fun one: every point in the strict interior of a triangle is a 1/3 centerpoint (and it generalizes to a 1/d centerpoint in d dimensions). This is the worst case for arbitrary sets of points, so if someone demands a better centerpoint you can just show them a triangle.

[marzipan-pig.livejournal.com]

I love how your posts are becoming less and less comprehensible to me. Maybe you should have some kind of warning label before we click? You have to be this tall to understand this post?

I like the pretty colors, and the circle thing is cool.

[eub.livejournal.com]

I don't think it's a straight path to incomprehensibility, I think it's more like a mushroom trip maybe.

I liked Kimberling's intro to the Encyclopedia of Triangle Centers:

Long ago, someone drew a triangle and three segments across it. Each segment started at a vertex and stopped at the midpoint of the opposite side. The segments met in a point. The person was impressed and repeated the experiment on a different shape of triangle. Again the segments met in a point. The person drew yet a third triangle, very carefully, with the same result. He told his friends. To their surprise and delight, the coincidence worked for them, too. Word spread, and the magic of the three segments was regarded as the work of a higher power.