Divine Proportions: Rational Trigonometry To Un... Site

), 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

: The rational equivalent of the Cosine Law (using "cross" 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 ), 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: their quadrances must satisfy:

: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy: