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What is a centroid?

What is a centroid? Here are some definitions.

Noun
  1. (mathematics) The point at the centre of any shape, sometimes called centre of area or centre of volume. For a triangle, the centroid is the point at which the medians intersect. The co-ordinates of the centroid are the average (arithmetic mean) of the co-ordinates of all the points of the shape. For a shape of uniform density, the centroid coincides with the centre of mass which is also the centre of gravity in a uniform gravitational field.
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In this case the volume of the solid generated equals the product of the area of the region and the length of the path traversed by the centroid.
But our search of the literature did not uncover these exact formulas involving the centroid, even for three-dimensional space.
Centroid size was calculated by summing the squared distances from each of the 27 landmarks to a common centroid.
The value assigned for each cell is the value of Gaussian curvature at the cell centroid.
Rotations and reflections are rigid transformations and clearly transform the centroid in the asserted fashion.
This procedure designates a centroid point, along with geographical co-ordinates, for each postal code region.

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