Difference between revisions of "Euler line"

m
m (Euler's line moved to Euler line: The line doesn't belong to Euler, it's named after him. "The Euler line of a triangle.")
(No difference)

Revision as of 18:59, 4 November 2006

This article is a stub. Help us out by expanding it.

Let $ABC$ be a triangle, points $H, N, G, O, L$ as $\triangle ABC$'s orthocenter, nine-point center, centroid, circumcenter, De Longchamps point respectively, then these points are collinear(regardless of $\triangle ABC$'s shape). And the line passes through points $H, N, G, O, L$ is called as Euler line, which is named after Leonhard Euler.

An interesting property of distances between these points on the Euler line:

  • $OG:GN:NH\equiv2:1:3$