What is Improper rotation?
An '''improper rotation''' can be understood as an [[inversion]] followed by a proper [[rotation]]. Equivalently it is the combination of a rotation and an [[inversion in a point]] on the [[Axis (mathematics)|axis]]. Therefore it is also called a '''rotoinversion''' or '''rotary inversion'''. A simple example of an improper rotation in [[3D]] (but not in 2D) is a coordinate inversion: x goes to −x, y to −y and z to −z. Under this transformation, a and b go to −a and −b (by the definition of a [[vector]]), but p clearly does not change. (It follows that any improper rotation multiplies p by −1 compared to the rotation's effect on a true vector.) {{math-stub}} [[Category:Geometry]]