(

*Mathematics - Geometry*)

The

Euler line of a

triangle is defined to be a

line that passes through the following three points.

The three points coincide only for

equilateral triangles, in which case the line is not

well-defined. By the

theorem of Snapper, these points are always

collinear for any

triangle, and the

centroid is one-third the way from the

circumcenter to the

orthocenter. By the

nine point circle theorem, the nine-point circle center also lie on the

Euler line at the

midpoint of the

circumcenter and the

orthocenter.

There are 96 other centers of a triangle that also lie on the Euler line, out of the 1,114 centers listed at the encyclopedia of triangle centers at http://faculty.evansville.edu/ck6/encyclopedia/