It seems like since there is only 1 way to rotate in 2D, there is only 1 degree of freedom. Why does the degrees of freedom in rotations not scale linearly, why is there a jump from 1 degree to 3 degrees from 2D to 3D? How does this scale in higher dimensions?

Alan7996

We previously talked about how we can add "fourth dimension" to approximate non-linear transformations as linear transformations. Can rotation of these imaginary new coordinates hold any significance? If so, can we see an example of such case?

It seems like since there is only 1 way to rotate in 2D, there is only 1 degree of freedom. Why does the degrees of freedom in rotations not scale linearly, why is there a jump from 1 degree to 3 degrees from 2D to 3D? How does this scale in higher dimensions?

We previously talked about how we can add "fourth dimension" to approximate non-linear transformations as linear transformations. Can rotation of these imaginary new coordinates hold any significance? If so, can we see an example of such case?