Q=(x2−x1)2+(y2−y1)2cap Q equals open paren x sub 2 minus x sub 1 close paren squared plus open paren y sub 2 minus y sub 1 close paren squared 2. Replace angle with spread Angles are replaced by (
: These laws work in any coordinate system, including those used in Einstein's Special Relativity (Minkowski space). ✅ Answer Divine Proportions: Rational Trigonometry to Un...
Rational Trigonometry is a purely algebraic alternative to classical trigonometry that replaces distance and angle with and spread , allowing for exact geometric calculations without transcendental functions. Q=(x2−x1)2+(y2−y1)2cap Q equals open paren x sub 2
s=QoppositeQhypotenuses equals the fraction with numerator cap Q sub o p p o s i t e end-sub and denominator cap Q sub h y p o t e n u s e end-sub end-fraction The spread ranges from indicates parallel lines and indicates perpendicular lines. 3. Apply the Main Laws For three points to be collinear, their quadrances
: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy:
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
: The rational equivalent of the Cosine Law (using "cross"