Definition:Centroid/Triangle

Definition

Let $\triangle ABC$ be a triangle.

The centroid of $\triangle ABC$ is the point $G$ where its three medians $AL$, $MB$ and $CN$ meet.

Also known as

A centroid is also referred to as a center of mean position.

Some sources refer to it as a mean point.

Approaches to this subject from the direction of physics and mechanics can be seen referring to it as a center of gravity.

However, it needs to be noted that the latter is merely a special case of a centroid.

Beware that some sources use the term center of gravity even when approaching the topic from a pure mathematical perspective, which can cause confusion.

Also see

• Medians of Triangle Meet at Centroid, where the existence of the centroid is proved.

• Results about centroids of triangles can be found here.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $12$. Mean points and centres of gravity
• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {IV}$. Pure Geometry: Plane Geometry: The centre of gravity
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): centroid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): centroid
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): centroid (of a triangle)