X656

CROSSDIFFERENCE OF X1 AND X19

X656 = crossdifference of every pair of points on line {1, 19}
< 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) { 44, 513 }: Central Line L(44, 513) { 240, 522 }: Central Line L(240, 522) { 521, 810 }: Central Line L(521, 810) { 667, 832 }: Central Line L(667, 832) { 662, 1101 }: Central Line L(662, 1101) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_521 = ISOGONAL CONJUGATE OF X(108) (1.1224, 0.1534) X_810 = CROSSPOINT OF X(1) AND X(163) (3.1222, -0.5010) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_832 = ODD (1, 4) INFINITY POINT (1.0668, -0.0533) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_1101 = TRILINEAR SQUARE OF X(110) (0.5344, 0.4306) X_656 = CROSSDIFFERENCE OF X(1) AND X(19) (7.5714, -0.8554) A B C X44 X513 X240 X522 X521 X810 X667 X832 X662 X1101 X656 (a, b, c) = (5, 6, 7) | AB = 1

X656 (CROSSDIFFERENCE OF X1 AND X19) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\tan B - \tan C : \tan C - \tan A : \tan A - \tan B\)
Barycentrics: \(\sin A (\tan B - \tan C) : \sin B (\tan C - \tan A) : \sin C (\tan A - \tan B)\)
Search Value (6, 9, 13): \(-13.533966773000\)
▸ Alternate Coordinates5 forms

  • Trilinears: \(\sin 2B - \sin 2C : :\)

  • Trilinears: \(\cos A \sin(B - C) : :\)

  • Trilinears: \(b \cos(C - A) - c \cos(B - A) : :\)

  • Trilinears: \((b^{2} - c^{2})(b^{2} + c^{2} - a^{2}) : :\)

  • Trilinears: \(d(a,b,c) : :\), where d(a,b,c) = directed distance from A to Euler line

▸ Linear Combinations1 combination

  • X656 = \(2\) X1734 + X1769, \(3\) X2457 - \(2\) X7178, \(3\) X2457 - X23752, \(2\) X4036 - \(3\) X21052, X4064 - \(3\) X14429, \(2\) X7253 - \(3\) X45686, \(4\) X8062 - \(3\) X45686, \(3\) X11125 - \(2\) X44409, \(3\) X19875 - \(2\) X45660, \(3\) X41800 - X44409:math:>

▸ Incident Central Lines116 lines

{1, 7629}, {2, 7253}, {3, 23189}, {10, 4086}, {11, 38981}, {19, 8768}, {37, 4171}, {44, 513}, {48, 9253}, {63, 14209}, {65, 42768}, {69, 15419}, {71, 10099}, {75, 17893}, {100, 39026}, {101, 2722}, {108, 2762}, {109, 2766}, {115, 35091}, {122, 35580}, {125, 7004}, {162, 2633}, {201, 6368}, {240, 522}, {244, 8286}, {407, 42755}, {514, 23800}, {521, 810}, {523, 2457}, {525, 4064}, {647, 8611}, {662, 1101}, {663, 15313}, {667, 832}, {676, 6608}, {900, 6615}, {1021, 16612}, {1834, 23757}, {1924, 19559}, {1953, 9249}, {1955, 2616}, {2092, 3126}, {2310, 8287}, {2345, 4529}, {2523, 22383}, {2530, 6371}, {2605, 8674}, {2629, 9390}, {2972, 39004}, {3122, 21945}, {3139, 35015}, {3269, 16573}, {3667, 4129}, {3700, 6587}, {3709, 24290}, {3733, 5096}, {3737, 5127}, {3776, 13258}, {3837, 28116}, {3900, 6129}, {3914, 42767}, {3942, 20975}, {4010, 23301}, {4019, 4580}, {4025, 14208}, {4036, 21052}, {4122, 23954}, {4132, 4729}, {4139, 4730}, {4140, 21958}, {4151, 4815}, {4367, 38469}, {4391, 20316}, {4524, 7250}, {4575, 36061}, {4705, 8672}, {4778, 4905}, {4804, 30591}, {4811, 25009}, {4985, 8714}, {5224, 18160}, {5903, 35050}, {6332, 20315}, {6739, 24028}, {7254, 20746}, {7658, 21172}, {8057, 17094}, {9001, 43924}, {10015, 21102}, {11125, 41800}, {14077, 14353}, {14192, 37305}, {14288, 44316}, {14315, 28183}, {17496, 20293}, {18155, 24718}, {19875, 45660}, {21912, 22069}, {22084, 26932}, {22091, 23224}, {22342, 23286}, {22379, 23187}, {23738, 28195}, {24031, 34846}, {24410, 37041}, {24457, 28221}, {24893, 24921}, {25299, 27710}, {25440, 36033}, {30765, 42327}, {35069, 35116}, {35200, 36062}, {36031, 40577}, {36036, 46254}, {37154, 43728}, {40952, 42758}

▸ Functional Relations38 relations