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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 .
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 centre of a parabola is the contact point of the figurative straight. The centre of a hyperbola lies without the curve, since the figurative straight crosses the curve. The tangents from the centre to the hyperbola are called 'asymptotes'. Their contact points are the two points at infinity on the curve.
Figure 1: The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center. In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another.
The center of a group G consists of all those elements x in G such that xg = gx for all g in G. This is a normal subgroup of G. The similarly named notion for a semigroup is defined likewise and it is a subsemigroup. [1] [2] The center of a ring (or an associative algebra) R is the subset of R consisting of all those elements x of R such that ...
An infinite difference is a further generalization, where the finite sum above is replaced by an infinite series. Another way of generalization is making coefficients μ k depend on point x: μ k = μ k (x), thus considering weighted finite difference. Also one may make the step h depend on point x: h = h(x).
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