- published: 24 Apr 2016
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In geometry, the centre (or center) (from Greek κέντρο) of an object is a point in some sense in the middle of the object. If geometry is regarded as the study of isometry groups then the centre is a fixed point of the isometries.
The centre of a circle is the point equidistant from the points on the edge. Similarly the centre of a sphere is the point equidistant from the points on the surface, and the centre of a line segment is the midpoint of the two ends.
For objects with several symmetries, the centre of symmetry is the point left unchanged by the symmetric actions. So the centre of a square, rectangle, rhombus or parallelogram is where the diagonals intersect, this being (amongst other properties) the fixed point of rotational symmetries. Similarly the centre of an ellipse is where the axes intersect.
Main article : Triangle centre
Several special points of a triangle are often described as triangle centres: the circumcentre, centroid or centre of mass, incentre, excentres, orthocentre, nine-point centre. For an equilateral triangle, these (except for the excentres) are the same point, which lies at the intersection of the three axes of symmetry of the triangle, one third of the distance from its base to its apex.
Center or centre may refer to:
Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metria "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early as Thales (6th Century BC). By the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. Both geometry and astronomy were considered in the classical world to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.