Rotation by reflection

This diagram illustrates how the rotation x -> x'' in can be constructed by two successive reflections at planes (blue and red) which enclose half the angle of the desired rotation angle. Only the component xs of the vector x in the plane of the two vectors n and m is affected. It is therefore sufficient to only be concerned with this plane perpendicular to the axis of rotation. Change the vectors interactively by dragging the red points.

This also illustrates rotation behavior of a spinor!

Please enable Java for an interactive construction (with Cinderella).

Compare the simple plane case.

[ GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).