Centroid

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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 ${\displaystyle n}$-dimensional Euclidean space.^[1]

In geometry, one often assumes uniform mass density, in which case the barycenter or center of mass coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin.^[2]

In physics, if variations in gravity are considered, then a center of gravity can be defined as the weighted mean of all points weighted by their specific weight.

In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center.