You'll need to ask an actual mathematician. Cook recently wrote that blog post, so it's much better to ask him in the comment section of that post. Just becaus

You'll need to ask an actual mathematician. Cook recently wrote that blog post, so it's much better to ask him in the comment section of that post. Just because I can do a Google Scholar query using "rational trigonometry" and find papers saying things like: "Explicit tough Ramsey graphs" at https://arxiv.org/pdf/0807.2692.pdf https://arxiv.org/pdf/0807.2692.pdf . "We present here two new explicit constructions ... The first construction is based on a remarkable new approach of Wildberger to trigonometry and Euclidean geometry." does not mean I am qualified to judge what is "interesting", or figure out which use non-real fields.