Скачать или смотреть Five Main Laws of Rational Trig | Rational Trigonometry | N J Wildberger

Here are the five main laws of (planar) Rational Trigonometry, which all follow from the Cross law. We derive these in a simple fashion. The laws are

Pythagoras' theorem
Triple quad formula
Cross law
Spread law
Triple spread formula

These replace the transcendental laws that students learn in a usual trigonometry course -- including the Cosine Law, the Sine law, and the "Sum of angles equals pi" formula. Here everything is rational, algebraic, and calculable. And the laws extend not only to arbitrary fields (including finite fields!) but also to more general quadratic forms, including relativistic (Lorentz) geometries

Video Contents: (thanks to buzzwatch2025)

00:00 Introduction to Rational Trig
2:18 Quadrance and Spread: Replacing Distance and Angle
7:27 Statement of the Cross Law
16:01 Pythagoras’ Theorem in Rational Trigonometry
24:05 The Triple Spread Formula: A Surprising Cubic Relationship
29:04 Quadria: A Hidden Quantity Related to Area
30:00 Final Thoughts: A New Way to Teach Geometry

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