Category:Definitions/Centroids
This category contains definitions related to Centroids.
Related results can be found in Category:Centroids.
Let $S = \set {A_1, A_2, \ldots, A_n}$ be a set of $n$ points in Euclidean space.
Definition 1
Let the position vectors of the elements of $S$ be given by $\mathbf a_1, \mathbf a_2, \dotsc, \mathbf a_n$ respectively.
Let $G$ be the point whose position vector is given by:
- $\vec {OG} = \dfrac 1 n \paren {\mathbf a_1 + \mathbf a_2 + \dotsb + \mathbf a_n}$
Then $G$ is known as the centroid of $S$.
Definition 2
Let the Cartesian coordinates of the elements of $S$ be $\tuple {x_j, y_j, z_j}$ for each $j \in \set {1, 2, \ldots, n}$.
Let $G$ be the point whose Cartesian coordinates are given by:
- $G = \tuple {\dfrac 1 n \ds \sum_{j \mathop = 1}^n x_j, \dfrac 1 n \ds \sum_{j \mathop = 1}^n y_j, \dfrac 1 n \ds \sum_{j \mathop = 1}^n z_j}$
That is, the arithmetic mean of the Cartesian coordinates of the elements of $S$
Then $G$ is known as the centroid of $S$.
Pages in category "Definitions/Centroids"
The following 15 pages are in this category, out of 15 total.
C
- Definition:Centroid
- Definition:Centroid of Set of Points
- Definition:Centroid of Set of Points/Definition 1
- Definition:Centroid of Set of Points/Definition 2
- Definition:Centroid of Solid Figure
- Definition:Centroid of Surface
- Definition:Centroid of Triangle
- Definition:Centroid of Weighted Set of Points
- Definition:Centroid/Also known as
- Definition:Centroid/Set of Points
- Definition:Centroid/Solid Figure
- Definition:Centroid/Surface
- Definition:Centroid/Triangle
- Definition:Centroid/Weighted Set of Points