Chromogeometry (2008)

There is an interesting correspondence between red, green and blue geometries and hypercomplex numbers.

The quadratic form in Blue is the norm squared of the complex numbers.

The quadratic form in Red is the norm squared of the split-complex numbers.

The quadratic form in Green is the norm squared of R⊕R, which is isomorphic to the split-complex numbers.

There's also the dual numbers. They're the only remaining 2d unitary algebra over the Real numbers, but they don't feature in the above paper.

Wildberger is a very curious person. I have watched many of his YouTube videos and read some of his papers and I find them very interesting. But be careful, don't take too seriously his contempt towards established math.

If you're on a phone, here's a responsive HTML version: https://www.arxiv-vanity.com/papers/0806.3617/