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The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
The term "centroid" was coined in 1814. [3] It is used as a substitute for the older terms "center of gravity" and "center of mass" when the purely geometrical aspects of that point are to be emphasized.
The position coordinates x j and x k are replaced by their relative position r jk = x j − x k and by the vector to their center of mass R jk = (m j q j + m k q k)/(m j + m k). The node in the binary tree corresponding to the virtual body has m j as its right child and m k as its left child. The order of children indicates the relative ...
The three-dimensional coordinates of the center of mass are determined by performing this experiment twice with the object positioned so that these forces are measured for two different horizontal planes through the object. The center of mass will be the intersection of the two lines L 1 and L 2 obtained from the two experiments.
Barycentric coordinates are strongly related to Cartesian coordinates and, more generally, affine coordinates.For a space of dimension n, these coordinate systems are defined relative to a point O, the origin, whose coordinates are zero, and n points , …,, whose coordinates are zero except that of index i that equals one.
A four-dimensional orthotope is likely a hypercuboid. [7]The special case of an n-dimensional orthotope where all edges have equal length is the n-cube or hypercube. [2]By analogy, the term "hyperrectangle" can refer to Cartesian products of orthogonal intervals of other kinds, such as ranges of keys in database theory or ranges of integers, rather than real numbers.
A cube is a special case of rectangular cuboid in which the edges are equal in length. [1] Like other cuboids, every face of a cube has four vertices, each of which connects with three congruent lines. These edges form square faces, making the dihedral angle of a cube between every two adjacent squares being the interior angle of a square, 90 ...
A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. [1] [2] General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles.