CENTRE (GEOMETRY)

In geometry, the 'centre' (or 'center', in American English) 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.

Contents

Circles

Symmetric objects

Triangles

See also

Circles

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.

Symmetric objects

For objects with several symmetries, the center 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.

Triangles

Several special points of a triangle are often described as 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.

See also

★ Fixed points of isometry groups in Euclidean space