Editing Centroid (section)

{{Short description|Mean position of all the points in a shape}}
{{more footnotes|date=April 2013}}
[[Image:Triangle.Centroid.svg|thumb|right|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 of a function|arithmetic mean]] [[position (geometry)|position]] of all the points in the figure. The same definition extends to any object in <math>n</math>-[[dimension]]al [[Euclidean space]].<ref name = protter520>{{harvtxt|Protter|Morrey|1970|p=520}}</ref>

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.<ref>{{harvtxt|Protter|Morrey|1970|p=521}}</ref>

In physics, if variations in [[gravity]] are considered, then a ''[[center of gravity]]'' can be defined as the [[weighted mean]] of all points [[Weighting|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]].