I had a novel (I think) realization about Euler Lines that I think may lead to a new proof WRT the circumcenter, orthocenter, and centroid.

The theory right now (which I tested with a crude simulation) is that if you take an equilateral 2d triangle and represent it in 3d space. Then draw a line perpendicular to the plane of the triangle and through its center. Then as you change perspective in the 3d space so that the angles of the triangle are distorted to appear to match some arbitrary triangle then the apparent orientation of the line will match the Euler Line as it would be drawn classically (in 2D).

So if i can represent the points as 3D values using complex numbers I think i can do some fancy math to calculate these points and the euler line in a novel new way.