Posts tagged 'perspectivity'

W.22 Projective Cross-Ratio, Harmonic Pencils & The Pappus Bridge

If four concurrent lines r_1, r_2, r_3, r_4 through O_p meet a transversal l_a at collinear points A_1, A_2, A_3, A_4 and another transversal l_b at B_1, B_2, B_3, B_4, then the squared cross-ratio in quadrances (Q(A_1, A_3)*Q(A_2, A_4)) / (Q(A_1, A_4)*Q(A_2, A_3)) equals the pencil spread cross-ratio (s_13 * s_24) / (s_14 * s_23) and is invariant across all transversals.