centroid

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.

   центро́идcentróid, барице́нтрbaricéntr, центр тя́жестиcentr tjážesti

2. (конкретно)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.

   The centroid of an arbitrary function f is given by #92;frac#123;#92;intxf(x)dx#125;#123;#92;intf(x)dx#125;, where the integrals are calculated over the domain of f.

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.

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