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'centroid'
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| Title of object: |
centroid |
| Canonical Name: |
Centroid |
| Type: |
Definition |
| Created on: |
2001-10-31 00:35:23 |
| Modified on: |
2002-02-01 01:08:34 |
| Classification: |
msc:51-00 |
| Synonyms: |
centroid=barycenter
centroid=center of gravity |
Revision comment (for changes between this and next version):
| Changes for correction #10188 ('emphasis on defined terms'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
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Content:
The \emph{centroid} of a triangle (also called center of gravity of the triangle) is the point where the three medians intersect each other.
\begin{center}
\includegraphics{centroid}
\end{center}
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
$$AG=2GA'\quad BG=2GB'\quad CG=2GC'.$$ |
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