Euler's line
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| Image:Triangle.EulerLine.svg Euler's line
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In geometry, Euler's line (red line in the image), named after Leonhard Euler, is the line passing through the orthocenter (blue), the circumcenter (green), the centroid (yellow), and the center of the nine-point circle (red point) of any triangle.
Leonhard Euler showed that in any triangle, those four points are collinear. The center of the nine-point circle lies midway between the orthocenter and the circumcenter, and the distance from the centroid to the circumcenter is half that from the centroid to the orthocenter.
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External links
- Altitudes and the Euler Line at cut-the-knot
- Euler Line and 9-Point Circle at cut-the-knotde:Eulersche Gerade
es:Recta de Euler fr:Droite d'Euler hu:Euler-egyenes ja:オイラー線 ru:Прямая Эйлера zh:歐拉線