FamousMathProbs13d: The rotation problem and Hamilton's discovery of quaternions IV

We show how to practically implement the use of quaternions to describe the algebra of rotations of three dimensional space. The key idea is to use the notion of half-turn instead of angle: this is well suited to connect with the lovely algebraic structure of quaternions. The theory of half turns is interesting in its own right, and belongs to what we call Vector Trigonometry--an interesting variant of Rational Trigonometry that we intend to describe in detail elsewhere. Here we only need a few formulas fo