Proportions: Rational Trigonometry To Un... — Divine

(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.

: The rational equivalent of the Cosine Law (using "cross" Divine Proportions: Rational Trigonometry to Un...

: Computers are much faster at adding and multiplying than calculating trigonometric series. (Q1+Q2−Q3)2=4Q1Q2(1−s3)open paren cap Q sub 1 plus cap

Rational trigonometry simplifies classical laws into polynomial forms that are much easier for computers and students to manipulate: Unlike angles, which are circular, spread is a

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

), 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