X544
DIRECTION OF VECTOR AX + BX + CX, where X = X101
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) { 2, 101 }: Central Line L(2, 101) { 103, 376 }: Central Line L(103, 376) { 118, 381 }: Central Line L(118, 381) { 30, 511 }: Central Line L(30, 511) { 63, 1018 }: Central Line L(63, 1018)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1018 = -CROSS CONJUGATE OF X(1) (0.1051, 0.4358) X_544 = DIRECTION OF VECTOR AX + BX + CX, where X = X(101) (0.1236, 0.6161)
A
B
C
X2
X101
X103
X376
X118
X381
X30
X511
X63
X1018
X544
(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) { 2, 101 }: Central Line L(2, 101) { 103, 376 }: Central Line L(103, 376) { 118, 381 }: Central Line L(118, 381) { 30, 511 }: Central Line L(30, 511) { 63, 1018 }: Central Line L(63, 1018)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2 = CENTROID (0.5467, 0.1600) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.3077, 0.4615) X_103 = ANTIPODE OF X(101) (0.6923, -0.4615) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4533, -0.1600) X_118 = MIDPOINT OF X(4) AND X(101) (0.4738, 0.4708) X_381 = MIDPOINT OF X(2) AND X(4) (0.5933, 0.3200) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2569, -0.3367) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4286, 0.0000) X_1018 = -CROSS CONJUGATE OF X(1) (0.1391, 0.3652) X_544 = DIRECTION OF VECTOR AX + BX + CX, where X = X(101) (0.1895, 0.6106)
A
B
C
X2
X101
X103
X376
X118
X381
X30
X511
X63
X1018
X544
(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) { 2, 101 }: Central Line L(2, 101) { 103, 376 }: Central Line L(103, 376) { 118, 381 }: Central Line L(118, 381) { 30, 511 }: Central Line L(30, 511) { 63, 1018 }: Central Line L(63, 1018)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2 = CENTROID (0.5393, 0.1620) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.3365, 0.4725) X_103 = ANTIPODE OF X(101) (0.6635, -0.4725) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4607, -0.1620) X_118 = MIDPOINT OF X(4) AND X(101) (0.4773, 0.4792) X_381 = MIDPOINT OF X(2) AND X(4) (0.5787, 0.3239) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2881, -0.3552) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4401, 0.0000) X_1018 = -CROSS CONJUGATE OF X(1) (0.1799, 0.3985) X_544 = DIRECTION OF VECTOR AX + BX + CX, where X = X(101) (0.2249, 0.6434)
A
B
C
X2
X101
X103
X376
X118
X381
X30
X511
X63
X1018
X544
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) { 2, 101 }: Central Line L(2, 101) { 103, 376 }: Central Line L(103, 376) { 118, 381 }: Central Line L(118, 381) { 30, 511 }: Central Line L(30, 511) { 63, 1018 }: Central Line L(63, 1018)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2 = CENTROID (0.5444, 0.0934) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.4482, 0.2934) X_103 = ANTIPODE OF X(101) (0.5518, -0.8428) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4556, -0.6427) X_118 = MIDPOINT OF X(4) AND X(101) (0.5407, 0.5614) X_381 = MIDPOINT OF X(2) AND X(4) (0.5888, 0.4614) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_511 = ISOGONAL CONJUGATE OF X(98) (0.3235, -0.5244) X_63 = ISOGONAL CONJUGATE OF X(19) (0.3991, -0.1098) X_1018 = -CROSS CONJUGATE OF X(1) (0.2273, 0.2474) X_544 = DIRECTION OF VECTOR AX + BX + CX, where X = X(101) (0.2601, 0.6846)
A
B
C
X2
X101
X103
X376
X118
X381
X30
X511
X63
X1018
X544
Kimberling (6, 9, 13) | AB = 1
X544 (DIRECTION OF VECTOR AX + BX + CX, where X = X101 ) 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 \(f(a,b,c) = (2ax - by - cz)/a\) , \(x = x(a,b,c) = a/(b - c)\) , \(y = x(b,c,a)\) , \(z = x(c,a,b)\)
▸ Incident Central Lines7 lines
{2 101 30 511 63 1018 103 376 118 381 152 3543 3022 3058
▸ Functional Relations1 relation
