: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy:
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. Divine Proportions: Rational Trigonometry to Un...
Rational trigonometry simplifies classical laws into polynomial forms that are much easier for computers and students to manipulate: : Replaces the Triangle Inequality
is a revolutionary approach to geometry developed by Dr. Norman J. Wildberger that replaces transcendental functions like tantangent Norman J
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
(Q1+Q2+Q3)2=2(Q12+Q22+Q32)open paren cap Q sub 1 plus cap Q sub 2 plus cap Q sub 3 close paren squared equals 2 open paren cap Q sub 1 squared plus cap Q sub 2 squared plus cap Q sub 3 squared close paren : The rational equivalent of the Sine Law:
: Computers are much faster at adding and multiplying than calculating trigonometric series.