Political Calculations: Rewriting the Rules of Math

"Trigonometry has for centuries been difficult for students to learn. Part of the reason is that the foundations of the subject are problematic, relying on vague pictorial definitions of the key concepts of angles and trigonometric functions. That means students rarely come to grips with the logical structure of the theory. Rational trigonometry is much simpler, relying on the fundamental quadratic notions of quadrance and spread, and with basic laws that can be derived completely rigorously using only elementary algebra."