: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy:
is a revolutionary approach to geometry developed by Dr. Norman J. Wildberger that replaces transcendental functions like tantangent
(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:
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.
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
: Computers are much faster at adding and multiplying than calculating trigonometric series.
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
: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy:
is a revolutionary approach to geometry developed by Dr. Norman J. Wildberger that replaces transcendental functions like tantangent Divine Proportions: Rational Trigonometry to Un...
(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: : Replaces the Triangle Inequality
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. 3. Apply the Main Laws
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
: Computers are much faster at adding and multiplying than calculating trigonometric series.
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