Divine Proportions: Rational Trigonometry To Un... ❲2026 Edition❳

(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.

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...

Rational trigonometry simplifies classical laws into polynomial forms that are much easier for computers and students to manipulate: (Q1+Q2−Q3)2=4Q1Q2(1−s3)open paren cap Q sub 1 plus cap

: These laws work in any coordinate system, including those used in Einstein's Special Relativity (Minkowski space). ✅ Answer By avoiding irrational numbers and infinite series, it

(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:

is a revolutionary approach to geometry developed by Dr. Norman J. Wildberger that replaces transcendental functions like tantangent