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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.
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]
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 Euler lines of the 10 triangles with vertices chosen from A, B, C, F 1 and F 2 are concurrent at the centroid of triangle ABC. [ 12 ] The Euler lines of the four triangles formed by an orthocentric system (a set of four points such that each is the orthocenter of the triangle with vertices at the other three points) are concurrent at the ...
By comparison the circumcircle of a triangle is another circumconic that touches the triangle at its vertices, but is not centered at the triangle's centroid unless the triangle is equilateral. The area of the Steiner ellipse equals the area of the triangle times 4 π 3 3 , {\displaystyle {\frac {4\pi }{3{\sqrt {3}}}},} and hence is 4 times the ...
The triangle DEF is called the pedal triangle of P. [17] The antipedal triangle of P is the triangle formed by the lines through A, B, C perpendicular to PA, PB, PC respectively. Two points P and Q are called counter points if the pedal triangle of P is homothetic to the antipedal triangle of Q and the pedal triangle of Q is homothetic to the ...
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.
In plane geometry, the Morley centers are two special points associated with a triangle.Both of them are triangle centers.One of them called first Morley center [1] (or simply, the Morley center [2]) is designated as X(356) in Clark Kimberling's Encyclopedia of Triangle Centers, while the other point called second Morley center [1] (or the 1st Morley–Taylor–Marr Center [2]) is designated ...