Posts tagged 'grammola'

W.20 Metrical Conics: Circles, Ribbons, Parabolas, Quadrolas & Grammolas

A conic is the zero locus of a quadratic polynomial proportion C = <a:b:c:d:e:f>; metrically, Q(X, l) = R defines a ribbon, Q(X, F_0) = Q(X, l_dir) defines a parabola, the squared-sum/difference bifocal locus A(Q(X, F_1), Q(X, F_2), S) = 0 defines a quadrola (unifying ellipses and hyperbolas into one irreducible algebraic curve), and Q(X, l_1) +/- Q(X, l_2) = R defines a grammola.