Octonions

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. Octonions are useful for describing rotations in 3-dimensional space.

Quaternions were invented by Cayley, and are hence sometimes called Cayley numbers.