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Let $\triangle ABC$ be a triangle which is not equilateral.
The Euler line of $\triangle ABC$ is the straight line through the orthocenter, centroid and circumcenter of $\triangle ABC$.
In the above, the line $OGK$ is the Euler line of $\triangle ABC$.
- Position of Centroid on Euler Line
- Orthocenter, Centroid and Circumcenter Coincide iff Triangle is Equilateral
Source of Name
This entry was named for Leonhard Paul Euler.
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Euler line
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Euler line
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Euler line