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In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid , circumcenter , incenter and orthocenter were familiar to the ancient Greeks , and can be obtained by simple constructions .
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.
A triangle's centroid is the point that maximizes the product of the directed distances of a point from the triangle's sidelines. [ 20 ] Let A B C {\displaystyle ABC} be a triangle, let G {\displaystyle G} be its centroid, and let D , E , F {\displaystyle D,E,F} be the midpoints of segments B C , C A , A B , {\displaystyle BC,CA,AB,} respectively.
The Nagel point is the isotomic conjugate of the Gergonne point.The Nagel point, the centroid, and the incenter are collinear on a line called the Nagel line.The incenter is the Nagel point of the medial triangle; [2] [3] equivalently, the Nagel point is the incenter of the anticomplementary triangle.
English: This is a vector graphic version of Triangle.Centroid.png by Herbee which was licensed under the GFDL. Русский: Медианы и центроид треугольника Date
SVG version of Image:Triangle_centroid_2.PNG: Date: 15 March 2007: Source: Original uploader was K. Aainsqatsi at en.wikipedia: Author: Original Drawing: K. Aainsqatsi Simplified version: Rubber Duck (☮ • ) Permission (Reusing this file)
the centroid or centre of mass, the point on which the triangle would balance if it had uniform density; the incentre, the centre of the circle that is internally tangent to all three sides of the triangle; the orthocentre, the intersection of the triangle's three altitudes; and
A triangle centroid is a center of mass location such that it would balance on a pencil tip. The simulation need only add a centroid dimension to the physics parameters. Given centroid points in both object and target it is possible to define the line segment connecting these two points.