# Definition:Centroid/Triangle

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## 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)