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by h-cobordism
2239 days ago
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> Does such a thing exist at higher dimensions? Yes, everything in your first paragraph extends to any number of dimensions (replacing "quaternion" with "rotor"). > I vaguely recall something about having complex numbers for 2D rotation, quaternions for 3D rotation, and octonions for (I'm guessing) 4D rotation Bivectors and rotors faithfully represent rotations in any number of dimensions. The octonion product can't, because as you said, it's not associative, but rotations obviously have to compose associatively. |
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