It generalizes the notion of vectors as a continuum between scalars (0-dimensional) and volumes (n-dimensional where you chose the dimension of your space as n)

It generalizes the notion of vectors as a continuum between scalars (0-dimensional) and volumes (n-dimensional where you chose the dimension of your space as n) For example in a 3D space: * 0D: scalars * 1D: regular vectors, representing a point. * 2D: 'rotors', representing an oriented surface. These are equivalent to quaternions, in a generalized elegant manner. We use quaternions in 3D engines to have rotations that don't have a special axis like Euler's. * 3D: representing an oriented volume. Here's a link if you want to know more: https://marctenbosch.com/quaternions/ https://marctenbosch.com/quaternions/