In geometry, the centroid or barycenter of an object X in n-dimensional space is the intersection of all hyperplanes that divide X into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of X. In physics, the words centroid and barycenter may mean either the center of mass or the center of gravity of an object, depending on ...

Including:

• Centroid - Centroid of triangle and tetrahedon
• Centroid - Centroids of cones and pyramids
• Centroid - Centroid and convexity
• Centroid - Integral formula
• Centroid - Center of symmetry
• Centroid - Physical centroids

Read more here: » Centroid: Encyclopedia - Centroid

The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). The centroid divides each of the medians in the ratio 2:1. The centroid is the triangle's center of mass if the triangle is made from a uniform sheet of material. Its Cartesian coordinates are the means of the coordinates of the three vertices. A similar result holds for a tetrahedron: its centroid is the intersection of all line segments that connect each vertex to the centroid of the o ...

See also:

Centroid, Centroid - Centroid of triangle and tetrahedon, Centroid - Centroids of cones and pyramids, Centroid - Centroid and convexity, Centroid - Integral formula, Centroid - Center of symmetry, Centroid - Physical centroids

Read more here: » Centroid: Encyclopedia II - Centroid - Centroid of triangle and tetrahedon

The abscissa of the centroid of a plane figure can be given as the integral , where f(x) is the vertical extent of the object at abscissa x. The same formula yields the first coordinate of the centroid of an object in , for any dimension n, provided that f(x) is the (n − 1)-dimensional measure of the object's cross-section at coordinate See also:

Centroid, Centroid - Centroid of triangle and tetrahedon, Centroid - Centroids of cones and pyramids, Centroid - Centroid and convexity, Centroid - Integral formula, Centroid - Center of symmetry, Centroid - Physical centroids

Read more here: » Centroid: Encyclopedia II - Centroid - Integral formula