Glad to see Wildberger getting some recognition, even if some of it is mixed. His rational trigonometry is an entirely rigorous and interesting piece of mathematics even if you don't think it's particularly pragmatic.
This is my first time being exposed to this but I wonder. Is the rational trigonometry useful? As in, are there applications in which it would make a tangible impact, for example accelerating algorithms or making learning easier?
How does he deal with the diagonal of the square? because that needs sqrt(2).
He bases his metrical geometry on “quadrance” (squared distance) and “spread” (squared sine) rather than distance and angle measure.
Then, how does he deal with the the pentagon? because that needs sqrt(5+sqrt(5)) or something similar with two nested square roots.
To deal with pentagons you need to extend the field of rationals by an additional element. Wildberger is kind of ambivalent about finite field extensions.