Divine Proportions: Rational - Trigonometry To Un...

: Computers are much faster at adding and multiplying than calculating trigonometric series.

In rational trigonometry, we do not use "distance" (which often involves square roots). Instead, we use ( ), which is the square of the distance. For two points 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: : Computers are much faster at adding and

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 not just the real numbers. 1.

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

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

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 (