> Oh, my God. He has written a book on it. I hope its not part of the UNSW > pure mathemtics syllabus.
Wildberger is the guy who is promoting the idea that we should start off in geometry by doing it over vector spaces of the rationals, and then replacing all formulas which lead out of the rationals by things which do some of the same work but confine themselves to rational values. Instead of the norm, you use the associated bilinear and quadratic forms; he calls the square of the distance between two points "quadrance". Instead of angles, we can use "spread", which is sin^2(theta). Then multiple angle formulas involve a transformed version of the Chebychev polynomials, transferring from the [-1,1]^2 square to the [0,1]^2 square, which he calls "spread polynomials".
This is a cute idea but he wrecks it somewhat by rants about the "wrong" trigonometry and how terribly, terribly revolutionary this fairly obvious idea is.