Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the two representations. Actually this simple use of "quaternions" was first presented by Euler some seventy years earlier than Hamilton to solve the problem of "magic squares." For this reason the dynamics community commonly refers to quaternions in this application as "Euler parameters". A unit quaternion can be described as: where is a simple rotation angle and , , are the "direction cosines" locating the axis of rotation (Euler's Theorem).