TITLE: What is the motivation for quaternions?
QUESTION [36 upvotes]: I know imaginary numbers solve $x^2 +1=0$, but what is the motivation for quaternions?

REPLY [4 votes]: A modern motivation is to model 3D orientation and rotation in computer graphics. If you use the simple model of Euler angles, you may run into a problem: gimbal lock. Quaternions (and rotation matrices) avoid this.