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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. 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.
A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set of fixed points is either empty or an affine space . For an object, any unique centre and, more generally, any point with unique properties with respect to the object is a fixed point of its ...
The Steiner Inellipse. According to Marden's theorem, given the triangle with vertices (1, 7), (7, 5), (3, 1), the foci of the inellipse are (3, 5) and (13/3, 11/3), since. In geometry, the Steiner inellipse, [ 1] midpoint inellipse, or midpoint ellipse of a triangle is the unique ellipse inscribed in the triangle and tangent to the sides at ...
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In geometry, the Steiner ellipse of a triangle, also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse ( ellipse that touches the triangle at its vertices) whose center is the triangle's centroid. [ 1] Named after Jakob Steiner, it is an example of a circumconic.
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Nine-point circle (centered at nine-point center N which, along with H, G, O, lies on the Euler line e) 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 ...