Divine Proportions: Rational Trigonometry To Un... [360p]

: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy:

Rational trigonometry simplifies classical laws into polynomial forms that are much easier for computers and students to manipulate: Divine Proportions: Rational Trigonometry to Un...

with purely algebraic concepts. By avoiding irrational numbers and infinite series, it allows for exact calculations over any field, not just the real numbers. 1. Replace distance with quadrance : Replaces the Triangle Inequality

In rational trigonometry, we do not use "distance" (which often involves square roots). Instead, we use ( ), which is the square of the distance. For two points we use ( )