Centre (geometry)

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"Centre" and "Center" redirect here. For other uses, see: Center (disambiguation).

In geometry, the centre 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.

1 Circles
2 Symmetric objects
3 Triangles
4 See also

[edit] 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.

[edit] Symmetric objects

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.

[edit] 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.