Rational trigonometry

Wikipedia carries this entry on a new system of Trigonometry, to replace what we all learned in School. From the entry:


Rational trigonometry is a modern envisioning of trigonometry by Dr. Norman Wildberger of The University of New South Wales, explained in his book Divine Proportions: Rational Trigonometry to Universal Geometry.

Instead of distance and angle, it uses as its fundamental units quadrance (square of distance) and spread (square of sine of angle). This choice of variables enables calculations without square roots and trigonometric functions that generate irrational numbers - hence the name. For distinction, he refers to the traditional trigonometry as classical trigonometry.

It is otherwise broadly based on Cartesian analytic geometry, with a point defined as an ordered pair (x,y) and a line as a general linear equation Ax + By + C = 0.


It looks kind of cool. I get the feeling that it would feel weird to
use his approach for someone trained in "classical" trigonometry (his
term), until you grok it, then it would be really smooth.