Difference between revisions of "Euler line"
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| + | Let <math>ABC</math> be a triangle, points <math>H, N, G, O, L</math> as <math>\triangle ABC</math>'s [[orthocenter]], [[nine-point center]], [[centroid]], [[circumcenter]], [[De Longchamps point]] respectively, then these points are collinear(regardless of <math>\triangle ABC</math>'s shape). And the line passes through points <math>H, N, G, O, L</math> is called as Euler line, which is named after [[Leonhard Euler]]. | ||
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| + | An interesting property of distances between these points on the Euler line: | ||
| + | * <math>OG:GN:NH\equiv2:1:3</math> | ||
Revision as of 17:51, 4 November 2006
This article is a stub. Help us out by expanding it.
Let 
be a triangle, points 
as 
's orthocenter, nine-point center, centroid, circumcenter, De Longchamps point respectively, then these points are collinear(regardless of 's shape). And the line passes through points is called as Euler line, which is named after Leonhard Euler.
An interesting property of distances between these points on the Euler line:
