Definition:Euler Line

Definition

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 $\triangle ABC$.

Also see

• Position of Centroid on Euler Line
• Orthocenter, Centroid and Circumcenter Coincide iff Triangle is Equilateral

• Results about the Euler line can be found here.

Source of Name

This entry was named for Leonhard Paul Euler.

Sources

• 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