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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 Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. This resource is hosted at the University of Evansville . It started from a list of 400 triangle centers published in the 1998 book Triangle Centers and Central Triangles by Professor Clark Kimberling .
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 following result can be used to locate the Spieker center of any triangle. [1] The Spieker center of triangle ABC is the incenter of the medial triangle of ABC. That is, the Spieker center of ABC is the center of the circle inscribed in the medial triangle of ABC. This circle is known as the Spieker circle. The Spieker center is also ...
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 figure. The same definition extends to any object in -dimensional Euclidean space. [1]
The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. [3]
Fig 1. Construction of the first isogonic center, X(13). When no angle of the triangle exceeds 120°, this point is the Fermat point. In Euclidean geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible [1] or ...
c2) The Steiner inellipse of a triangle is the scaled Steiner Ellipse with scaling factor 1/2 and the centroid as center. Hence both ellipses have the same eccentricity , are similar . d) The area of the Steiner inellipse is π 3 3 {\displaystyle {\tfrac {\pi }{3{\sqrt {3}}}}} -times the area of the triangle.