# centroid

> English word · Noun · frequency rank #77,517

## Definitions
1. The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.
2. The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.
3. the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.
4. An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.
5. the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.
6. Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.

## Etymology
From centre + -oid. From 1844, used as a replacement for the older terms "centre of gravity" and "centre of mass" in situations described in purely geometrical terms, and subsequently used for further generalisations.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/centroid