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7/10/2025, 11:55:33 AM
>>16721115
Hamilton’s original question that led to the real quaternions was basically “you know i, the square root of -1? what if we put two i’s instead of just one”. He was obsessed with this question apparently. Yeah I think he was autistic. Anyway that’s one way of looking at the matter. The frobenius theorem is its natural endpoint.
The other common thing is just the quaternion group (as opposed to the real quaternions) as representing these rotations of a cube. You can verify with an actual cube if you want that the defining identities hold ij=k^-1 etc.
Hamilton’s original question that led to the real quaternions was basically “you know i, the square root of -1? what if we put two i’s instead of just one”. He was obsessed with this question apparently. Yeah I think he was autistic. Anyway that’s one way of looking at the matter. The frobenius theorem is its natural endpoint.
The other common thing is just the quaternion group (as opposed to the real quaternions) as representing these rotations of a cube. You can verify with an actual cube if you want that the defining identities hold ij=k^-1 etc.
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