The Frobenius theorem guarantees that these form the largest  nite-dimensional division ring, and they were the  rst discovered noncommutative division alge- bra.
These entities are not subject to gimbal lock, making them more useful than Euler angles. These form the only non-trivial central simple algebra over the reals, and are one of the two classes of the Brauer group of the reals. These can be constructed by performing the Cayley-Dickinson construction on the   complex numbers. Dividing one of these objects by its norm yields its versor. The Frobenius theorem guarantees that these form the largest  nite-dimensional division ring, and they were the  rst discovered noncommutative division alge- bra. For ten points, identify these four-dimensional analogues to the complex numbers.
These entities are not subject to gimbal lock, making them more useful than Euler angles.
quaternions