These entities are not subject to gimbal lock, making them more useful than Euler angles.
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