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centroid (Definition)

The centroid of a triangle (also called center of gravity of the triangle) is the point where the three medians intersect each other.

\includegraphics{centroid}

In the figure, $ AA', BB'$ and $ CC'$ are medians and $ G$ is the centroid of $ ABC$. The centroid $ G$ has the property that divides the medians in the ratio $ 2:1$, that is

$\displaystyle AG=2GA'\quad BG=2GB'\quad CG=2GC'.$



"centroid" is owned by drini. [ full author list (2) | owner history (1) ]
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See Also: median, orthocenter, triangle, Euler line, Ceva's theorem, triangle center, Lemoine point, Gergonne triangle, trigonometric version of Ceva's theorem

Other names:  barycenter, center of gravity

Attachments:
common point of triangle medians (Theorem) by pahio
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Cross-references: ratio, divides, property, intersect, medians, point, triangle
There are 16 references to this entry.

This is version 6 of centroid, born on 2001-10-31, modified 2006-11-03.
Object id is 647, canonical name is Centroid.
Accessed 13108 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
Pending Errata and Addenda
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