I love articles like this, but they all make the same mistake of starting with vector algebra instead of geometric algebra. In 3D space, vector algebra works, but it falls flat on its face in both 2D and 4D scenarios. It's intuitive until it is completely broken.
I would love to see the same style of article, but using bivectors and the like where appropriate, such that the whole thing generalises neatly to 4D space-time, not just 3D space.
I would love to see the same style of article, but using bivectors and the like where appropriate, such that the whole thing generalises neatly to 4D space-time, not just 3D space.