Quaternions and vectors. ... Take, for example, one of Maxwell's equations relating the electric and magnetic fields: ∇ × E = –∂B/∂t. With just a handful of symbols ...

I am asked whether the “spoonfeeding,” as he terms it, of Maxwell, Fitzgerald, &c., is not good enough for me. Why, of course not. It is quaternionic, and that is the real point concerned.

Hamilton called his 4D numbers "quaternions", and he used them to calculate geometrical rotations in 3D space. This is the kind of rotation used today to move a robot, say, or orient a satellite.

On the other hand, Lord Kelvin declared that quaternions, “though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell”.

Quaternions are vital for the control systems that guide aircraft and rockets. Let us think of an aircraft in flight. Changes in its orientation can be given by three rotations known as pitch, ...

Hamilton called his 4D numbers “quaternions”, and he used them to calculate geometrical rotations in 3D space. This is the kind of rotation used today to move a robot, say, or orient a satellite.