X536
DIRECTION OF VECTOR AX + BX + CX, where X = X37
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, 37 }: Central Line L(2, 37) { 44, 190 }: Central Line L(44, 190) { 30, 511 }: Central Line L(30, 511) { 335, 903 }: Central Line L(335, 903) { 894, 1100 }: Central Line L(894, 1100) { 1086, 1266 }: Central Line L(1086, 1266)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (1.0101, 0.0884) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_903 = -BLAIKIE TRANSFORM OF X(2) (1.0000, 0.0000) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_1266 = ISOTOMIC CONJUGATE OF X(1120) (2.8367, 1.7996) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727)
A
B
C
X739
X2
X37
X44
X190
X30
X511
X335
X903
X894
X1100
X1086
X1266
X536
(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, 37 }: Central Line L(2, 37) { 44, 190 }: Central Line L(44, 190) { 30, 511 }: Central Line L(30, 511) { 335, 903 }: Central Line L(335, 903) { 894, 1100 }: Central Line L(894, 1100) { 1086, 1266 }: Central Line L(1086, 1266)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (0.9869, 0.1139) X_2 = CENTROID (0.5467, 0.1600) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5787, 0.1787) X_44 = -LINE CONJUGATE OF X(1) (1.6000, 1.2000) X_190 = YFF PARABOLIC POINT (0.0933, 0.3200) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2569, -0.3367) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0641, 0.0374) X_903 = -BLAIKIE TRANSFORM OF X(2) (1.0000, 0.0000) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5637, 0.1831) X_1100 = COMPLEMENT OF X(319) (0.6103, 0.2103) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7733, 0.0800) X_1266 = ISOTOMIC CONJUGATE OF X(1120) (2.2800, 0.9600) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0502, -0.1300)
A
B
C
X739
X2
X37
X44
X190
X30
X511
X335
X903
X894
X1100
X1086
X1266
X536
(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, 37 }: Central Line L(2, 37) { 44, 190 }: Central Line L(44, 190) { 30, 511 }: Central Line L(30, 511) { 335, 903 }: Central Line L(335, 903) { 894, 1100 }: Central Line L(894, 1100) { 1086, 1266 }: Central Line L(1086, 1266)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (0.9964, 0.0601) X_2 = CENTROID (0.5393, 0.1620) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5661, 0.1805) X_44 = -LINE CONJUGATE OF X(1) (1.5111, 1.3165) X_190 = YFF PARABOLIC POINT (0.1322, 0.3610) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2881, -0.3552) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0000, 0.0000) X_903 = -BLAIKIE TRANSFORM OF X(2) (0.9465, -0.0371) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5538, 0.1856) X_1100 = COMPLEMENT OF X(319) (0.5928, 0.2126) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7429, 0.0625) X_1266 = ISOTOMIC CONJUGATE OF X(1120) (2.1219, 1.0180) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0667, -0.1655)
A
B
C
X739
X2
X37
X44
X190
X30
X511
X335
X903
X894
X1100
X1086
X1266
X536
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, 37 }: Central Line L(2, 37) { 44, 190 }: Central Line L(44, 190) { 30, 511 }: Central Line L(30, 511) { 335, 903 }: Central Line L(335, 903) { 894, 1100 }: Central Line L(894, 1100) { 1086, 1266 }: Central Line L(1086, 1266)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (0.9485, 0.0778) X_2 = CENTROID (0.5444, 0.0934) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5913, 0.1097) X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412) X_190 = YFF PARABOLIC POINT (0.1548, 0.2119) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_511 = ISOGONAL CONJUGATE OF X(98) (0.3235, -0.5244) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0278, 0.0074) X_903 = -BLAIKIE TRANSFORM OF X(2) (0.9340, -0.0252) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5611, 0.1167) X_1100 = COMPLEMENT OF X(319) (0.6266, 0.1395) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7392, 0.0341) X_1266 = ISOTOMIC CONJUGATE OF X(1120) (1.6862, 0.3633) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (-0.0753, -0.1221)
A
B
C
X739
X2
X37
X44
X190
X30
X511
X335
X903
X894
X1100
X1086
X1266
X536
Kimberling (6, 9, 13) | AB = 1
X536 (DIRECTION OF VECTOR AX + BX + CX, where X = X37 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \((2ax - by - cz)/a\) , where \(x = x(a,b,c) = b + c\) , \(y = x(b,c,a)\) , \(z = x(c,a,b)\)
Barycentrics: \(2bc - ca - ab : :\)
▸ Incident Central Lines12 lines
{2 37 30 511 42 2230 44 190 141 2321 335 903 889 3227 894 1100 1086 1266 2228 3123 2234 3009 2325 3008
▸ Functional Relations5 relations
