Octonions

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Octonions are an extension to the complex numbers, similar to quaternions. But whereas quaternions are quadruplets of real numbers, octonions are octets; and whereas in quaternions multiplication is not commutative, in octonions it isn't associative either.

The octonions were discovered by John T. Graves in 1843, and independently by Arthur Cayley, who published the first paper on them in 1845. They are sometimes called Cayley numbers.

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