← etc / Encyclopedia of Triangle Centers X2055–X2119 · Orion Transforms, Circumcircle Inverses, PK/NK Transforms, Reflections & Kepler Points / X_2058 ← Prev Overview · Code Next → X2058¶ ORION TRANSFORM OF X15 5, 6, 7 3, 4, 5 Kepler Kimberling < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2058 = ORION TRANSFORM OF X(15) (0.4673, 0.0312) A B C X2058 (a, b, c) = (5, 6, 7) | AB = 1 < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2058 = ORION TRANSFORM OF X(15) (0.4872, -0.0524) A B C X2058 (a, b, c) = (3, 4, 5) | AB = 1 < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2058 = ORION TRANSFORM OF X(15) (0.4892, -0.0530) A B C X2058 Kepler (1, √φ, φ) | AB = 1 < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2058 = ORION TRANSFORM OF X(15) (0.5975, -0.0051) A B C X2058 Kimberling (6, 9, 13) | AB = 1 X2058 (ORION TRANSFORM OF X15) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is given just above X2055, using X = X15 Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\) Search Value (6, 9, 13): \(3.227310880368\)
