Divine Proportions: Rational Trigonometry To Un... -

), a dimensionless ratio that measures the "separation" between two lines. Unlike angles, which are circular, spread is a rational function. For a right triangle with quadrances Q1cap Q sub 1 Q2cap Q sub 2 , and hypotenuse Q3cap Q sub 3

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 Divine Proportions: Rational Trigonometry to Un...

: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy: ), a dimensionless ratio that measures the "separation"

Rational trigonometry simplifies classical laws into polynomial forms that are much easier for computers and students to manipulate: By avoiding irrational numbers and infinite series, it

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

: 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