Difference between revisions of "Euler line"
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.") |
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An interesting property of distances between these points on the Euler line: | An interesting property of distances between these points on the Euler line: | ||
* <math>OG:GN:NH\equiv2:1:3</math> | * <math>OG:GN:NH\equiv2:1:3</math> | ||
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| + | Construct an [[orthic triangle]]<math>\triangle H_A,H_B,H_C</math>, then Euler lines of <math>\triangle AH_BH_C</math>,<math>\triangle BH_CH_A</math>,<math>\triangle CH_AH_B</math> concur at <math>\triangle ABC</math>'s [[nine-point center]]. | ||
Revision as of 20:27, 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:
Construct an orthic triangle
, then Euler lines of 
,
,
concur at 's nine-point center.
