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

[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.