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Centroid - Centroid of triangle and tetrahedon | | Centroid - Centroid of triangle and tetrahedon: Encyclopedia II - Centroid - Centroid of triangle and tetrahedon | | 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 | | | Centroid, Centroid - Center of symmetry, Centroid - Centroid and convexity, Centroid - Centroid of triangle and tetrahedon, Centroid - Centroids of cones and pyramids, Centroid - Integral formula, Centroid - Physical centroids, Pappus's centroid theorem | | |
| | | Centroid: Encyclopedia II - Centroid - Centroid of triangle and tetrahedon
Centroid - Centroid of triangle and tetrahedon
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 opposite face. These line segments are divided by the centroid in the ratio 3:1. The result generalizes to any n-dimensional simplex in the obvious way.
The isogonal conjugate of a triangle's centroid is its symmedian point.
Other related archivesCartesian coordinates, Pappus's centroid theorem, abscissa, apex, average, bowl, center of gravity, center of mass, concave, convex, density, dimensional, fixed point of all isometries, geometry, gravitational field, hyperplanes, isogonal conjugate, means, medians, physics, ratio, ring, simplex, space, symmedian point, symmetry, symmetry group, tetrahedron, translational symmetry, triangle, vertex
 Adapted from the Wikipedia article "Centroid of triangle and tetrahedon", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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