There are no non-trivial rotations in one dimension. In two dimensions, only a single angle is needed to specify a rotation about the origin – the "angle of rotation" that specifies an element of the circle group (also known as ). The rotation is acting to rotate an object counterclockwise through an angle about the origin; see below for details. Composition of rotations sums their angles modulo 1 turn, which implies that all two-dimensional rotations about "the same" point commute. Rotations about "different" points, in general, do not commute. Any two-dimensional direct motion is either a translation or a rotation; see Euclidean plane isometry for details.