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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?