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An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A ...
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object X {\displaystyle X} in n {\displaystyle n} - dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about the hyperplane.
Varignon's theorem is a theorem of French mathematician Pierre Varignon (1654–1722), published in 1687 in his book Projet d'une nouvelle mécanique. The theorem states that the torque of a resultant of two concurrent forces about any point is equal to the algebraic sum of the torques of its components about the same point.
Centroid of a triangle. In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in -dimensional Euclidean space. [1]
The center of the van Lamoen circle is point () in Clark Kimberling's comprehensive list of triangle centers. [1]In 2003, Alexey Myakishev and Peter Y. Woo proved that the converse of the theorem is nearly true, in the following sense: let be any point in the triangle's interior, and ′, ′, and ′ be its cevians, that is, the line segments that connect each vertex to and are extended until ...
The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices. The "side centroid" comes from considering the sides to have constant mass per unit length. The usual centre, called just the centroid (centre of area) comes from considering the surface of the polygon as having constant density ...
The NSYNC vocalist popped over to Studio 8H for the Nov. 15, 2008, episode hosted by Paul Rudd to try to help convince his "Until the End of Time" collaborator of the gold they had at their ...
Commandino's theorem, named after Federico Commandino (1509–1575), states that the four medians of a tetrahedron are concurrent at a point S, which divides them in a 3:1 ratio. In a tetrahedron a median is a line segment that connects a vertex with the centroid of the opposite face – that is, the