## Rotation

The turning of an object or coordinate system by an Angle about a fixed point. A rotation is an Orientation-Preserving Orthogonal Transformation. Euler's Rotation Theorem states that an arbitrary rotation can be parameterized using three parameters. These parameters are commonly taken as the Euler Angles. Rotations can be implemented using Rotation Matrices.

The rotation Symmetry Operation for rotation by is denoted ``.'' For periodic arrangements of points (``crystals''), the Crystallography Restriction gives the only allowable rotations as 1, 2, 3, 4, and 6.

See also Dilation, Euclidean Group, Euler's Rotation Theorem, Expansion, Improper Rotation, Infinitesimal Rotation, Inversion Operation, Mirror Plane, Orientation-Preserving, Orthogonal Transformation, Reflection, Rotation Formula, Rotation Group, Rotation Matrix, Rotation Operator, Rotoinversion, Shift, Translation

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 211, 1987.

Yates, R. C. ``Instantaneous Center of Rotation and the Construction of Some Tangents.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 119-122, 1952.