Divine Proportions: Rational - Trigonometry To Un...

: The rational equivalent of the Cosine Law (using "cross"

is a revolutionary approach to geometry developed by Dr. Norman J. Wildberger that replaces transcendental functions like tantangent Divine Proportions: Rational Trigonometry to Un...

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 : The rational equivalent of the Cosine Law

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 ( Divine Proportions: Rational Trigonometry to Un...

s1Q1=s2Q2=s3Q3the fraction with numerator s sub 1 and denominator cap Q sub 1 end-fraction equals the fraction with numerator s sub 2 and denominator cap Q sub 2 end-fraction equals the fraction with numerator s sub 3 and denominator cap Q sub 3 end-fraction