: These laws work in any coordinate system, including those used in Einstein's Special Relativity (Minkowski space). ✅ Answer
: Computers are much faster at adding and multiplying than calculating trigonometric series.
), 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 Divine Proportions: Rational Trigonometry to Un...
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.
: The rational equivalent of the Cosine Law (using "cross" : These laws work in any coordinate system,
is a revolutionary approach to geometry developed by Dr. Norman J. Wildberger that replaces transcendental functions like tantangent
(Q1+Q2−Q3)2=4Q1Q2(1−s3)open paren cap Q sub 1 plus cap Q sub 2 minus cap Q sub 3 close paren squared equals 4 cap Q sub 1 cap Q sub 2 open paren 1 minus s sub 3 close paren Why This Matters : You never need to use a calculator for 2the square root of 2 end-root . All results are exact fractions. Unlike angles, which are circular, spread is a
: Replaces the Triangle Inequality. For three points to be collinear, their quadrances must satisfy:
