Divine Proportions: Rational Trigonometry To Un... -

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

: Computers are much faster at adding and multiplying than calculating trigonometric series. Divine Proportions: Rational Trigonometry to Un...

: These laws work in any coordinate system, including those used in Einstein's Special Relativity (Minkowski space). ✅ Answer In rational trigonometry, we do not use "distance"

Rational trigonometry simplifies classical laws into polynomial forms that are much easier for computers and students to manipulate: : These laws work in any coordinate system,

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

), 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

(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: