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Centroid of a triangle. In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in -dimensional Euclidean space. [1]
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object X {\displaystyle X} in n {\displaystyle n} - dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about the hyperplane.
[7] An updated list of geographic centers using this definition (which is equivalent to the state's centroid) is given below. It was derived by minimizing the sum of squared great circle distances from all points of land in a state (including islands, but not coastal waters, following the earlier practice of the USGS). It represents a slight ...
Geometrically defined it is the centroid of all land surfaces within the two dimensions of the Geoid surface which approximates the Earth's outer shape. The term centre of minimum distance [ 1 ] specifies the concept more precisely as the domain is the sphere surface without boundary and not the three-dimensional body.
centroid of volume (incorporating elevations into calculations), instead of the more usual centroid of area as described above. [6] centre point of a bounding box completely enclosing the area. While relatively easy to determine, a centre point calculated using this method will generally also vary (relative to the shape of the landmass or ...
The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices. The "side centroid" comes from considering the sides to have constant mass per unit length. The usual centre, called just the centroid (centre of area) comes from considering the surface of the polygon as having constant density ...
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In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions.