Generalizations Euler's rotation theorem

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in higher dimensions, rigid motion preserve point in dimension 2n or 2n + 1 composition of @ n rotations in orthogonal planes of rotation, though these planes need not uniquely determined, , rigid motion may fix multiple axes.



a screw motion.


a rigid motion in 3 dimensions not fix point screw motion . because composition of rotation translation perpendicular axis rotation parallel axis, while composition translation parallel axis yields screw motion; see screw axis. gives rise screw theory.







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