Chromogeometry (2008)(arxiv.org)
arxiv.org
Chromogeometry (2008)
https://arxiv.org/abs/0806.3617
3 comments
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/
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.