Sometimes people say "Quaternions are 4 dimensional". They are trying to scare you. It's no more true than "3x3 matrices are 9 dimensional", and no more helpful either.There is a concrete, 3D way to visualize quaternions. Every quaternion is a mixture of some amount of axis line, and some amount of identity. On their own, axis lines do 180 rotations. On its own, the identity (the "w" coordinate of a quaternion) does a 0 rotation. Having a little of both lets you do rotations by other amounts.We'll use this to see how quaternions are created, interpolated, and composed together. Then we'll use the same approach to understand dual quaternions which, unlike quaternions, can translate, as well as rotate around lines that do not pass through the origin. We'll also see how all of this allows for bug-free animations to be done with code that is efficient and simple.