Posts tagged 'red metric'

W.23 Chromogeometry & Universal Symmetric Bilinear Forms

Replacing the Euclidean quadratic form with any non-degenerate symmetric bilinear form M on F^2 preserves all Five Laws of Rational Trigonometry; in Chromogeometry—pairing Blue (dx^2 + dy^2), Red (dx^2 - dy^2), and Green (2*dx*dy) metrics on the same triangle—the three Euler lines concur at the centroid G, C_B C_R O_B C_G is a parallelogram, and N_B = (C_R + C_G)/2.