Difference between revisions of "Euler line"

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#REDIRECT[[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:
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* <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 $ABC$ 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:

  • $OG:GN:NH\equiv2:1:3$
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