Rotation by reflection

This diagram illustrates how the rotation xs -> xs'' in can be constructed by two successive reflections at straight lines (blue and red) which enclose half the angle of the desired rotation angle. The entire event is taking place in the plane of the two vectors n and m. 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 rotation in three dimensions.

[ GA with Cinderella ]

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