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Explore the five main laws of planar Rational Trigonometry in this 31-minute educational video from Insights into Mathematics. Learn how these laws—Pythagoras' theorem, Triple quad formula, Cross law, Spread law, and Triple spread formula—all derive from the Cross law and replace the traditional transcendental trigonometric formulas. Discover a rational, algebraic, and calculable approach to trigonometry that extends beyond conventional applications to arbitrary fields (including finite fields) and more general quadratic forms, such as relativistic (Lorentz) geometries. This mathematical exploration offers an alternative to the standard trigonometry curriculum by presenting a system that eliminates transcendental functions while maintaining powerful geometric applications.
