The octonions aren’t even associative, making them less “natural” and harder to work with. But quaternions are quite useful for working with rotations in three

The octonions aren’t even associative, making them less “natural” and harder to work with. But quaternions are quite useful for working with rotations in three dimensions. To be very technical, the unit imaginary quaternions form a double (universal) cover of the rotation group SO(3).