Rotation is defined as rigid movement having as fixed points a point called center (in two dimensions) or a straight line called axis (in three dimensions) of rotation. This movement shifts all points around the center, or axis, by a fixed angle. In other words a rotation is the movement of a body following a circular trajectory. In two dimensions, ie on the plane, a figure can rotate around a point called the instant rotation center; in three dimensions, the rotation takes place around a straight line called the instant rotation axis and more generally, a rotation in \(n\) dimensions takes place around a space with \(n-2\) dimensions.
This formalizes the sensory perception according to which rotating a non-deformable object is equivalent to varying the angle of all its points by the same quantity, ie leaving the reciprocal angular relations unchanged. In particular, a rotation is a transformation that preserves the scalar product.