Rational Trigonometry/0

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This video is by Dr. Norman Wildberger, professor (emeritus) at the University of New South Wales. There are three fundamental branches of mathematics: arithmetic, algebra, and geometry. Geometry has fallen on hard times, so let us begin at the intersection of all three. The textbook will be Divine Proportions, the book by Dr. Wildberger.

Euclid's Elements was the foundation for a very long time, until people realized there were cracks in it. Following pictures (as opposed to rigorous proof and numbers) leads to faulty conclusions. This synthetic approach to geometry was superceded by the analytic approach to geometry, a purely algebraic approach via gridlines. Unfortunately, this approach too was flawed, relying on transcendental functions and concepts (such as angles and distance).