X1308
COLLINGS TRANSFORM OF X661
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) { 36, 105 }: Central Line L(36, 105) { 100, 514 }: Central Line L(100, 514) { 101, 513 }: Central Line L(101, 513) { 103, 517 }: Central Line L(103, 517) { 104, 516 }: Central Line L(104, 516) { 1, 840 }: Central Line L(1, 840)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3887 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.9920, 0.5711) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_1 = INCENTER (0.5714, 0.2333) X_840 = ISOGONAL CONJUGATE OF X(528) (0.0800, 0.3919) X_1308 = COLLINGS TRANSFORM OF X(661) (1.0102, 0.0916)
A
B
C
X3887
X36
X105
X100
X514
X101
X513
X103
X517
X104
X516
X1
X840
X1308
(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) { 36, 105 }: Central Line L(36, 105) { 100, 514 }: Central Line L(100, 514) { 101, 513 }: Central Line L(101, 513) { 103, 517 }: Central Line L(103, 517) { 104, 516 }: Central Line L(104, 516) { 1, 840 }: Central Line L(1, 840)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_3887 = com[INVERSE(n(3rd EULER TRIANGLE))] (1.0459, 0.4453) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.0000, 1.0000) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9800, -0.1400) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0889, -0.0314) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.3077, 0.4615) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_103 = ANTIPODE OF X(101) (0.6923, -0.4615) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8038, 0.6743) X_104 = ANTIPODE OF X(100) (0.8000, -0.4000) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7380, 0.7022) X_1 = INCENTER (0.6000, 0.2000) X_840 = ISOGONAL CONJUGATE OF X(528) (0.1000, 0.3000) X_1308 = COLLINGS TRANSFORM OF X(661) (0.9846, 0.1231)
A
B
C
X3887
X36
X105
X100
X514
X101
X513
X103
X517
X104
X516
X1
X840
X1308
(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) { 36, 105 }: Central Line L(36, 105) { 100, 514 }: Central Line L(100, 514) { 101, 513 }: Central Line L(101, 513) { 103, 517 }: Central Line L(103, 517) { 104, 516 }: Central Line L(104, 516) { 1, 840 }: Central Line L(1, 840)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_3887 = com[INVERSE(n(3rd EULER TRIANGLE))] (1.0592, 0.4077) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (0.9387, 1.0546) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9563, -0.2045) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0910, -0.0001) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.3365, 0.4725) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_103 = ANTIPODE OF X(101) (0.6635, -0.4725) X_517 = ISOGONAL CONJUGATE OF X(104) (0.7602, 0.6929) X_104 = ANTIPODE OF X(100) (0.7614, -0.4263) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7014, 0.7136) X_1 = INCENTER (0.5841, 0.2021) X_840 = ISOGONAL CONJUGATE OF X(528) (0.0333, 0.1794) X_1308 = COLLINGS TRANSFORM OF X(661) (0.9504, 0.2172)
A
B
C
X3887
X36
X105
X100
X514
X101
X513
X103
X517
X104
X516
X1
X840
X1308
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) { 36, 105 }: Central Line L(36, 105) { 100, 514 }: Central Line L(100, 514) { 101, 513 }: Central Line L(101, 513) { 103, 517 }: Central Line L(103, 517) { 104, 516 }: Central Line L(104, 516) { 1, 840 }: Central Line L(1, 840)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_3887 = com[INVERSE(n(3rd EULER TRIANGLE))] (1.1866, 0.2272) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (0.7120, 0.4690) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (1.0692, -0.3135) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_514 = ISOGONAL CONJUGATE OF X(101) (1.1917, -0.0133) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.4482, 0.2934) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_103 = ANTIPODE OF X(101) (0.5518, -0.8428) X_517 = ISOGONAL CONJUGATE OF X(104) (0.7243, 0.7243) X_104 = ANTIPODE OF X(100) (0.6794, -0.8162) X_516 = ISOGONAL CONJUGATE OF X(103) (0.6510, 0.7407) X_1 = INCENTER (0.6154, 0.1300) X_840 = ISOGONAL CONJUGATE OF X(528) (-0.0041, -0.0075) X_1308 = COLLINGS TRANSFORM OF X(661) (0.8436, 0.1807)
A
B
C
X3887
X36
X105
X100
X514
X101
X513
X103
X517
X104
X516
X1
X840
X1308
Kimberling (6, 9, 13) | AB = 1
X1308 (COLLINGS TRANSFORM OF X661 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above
X1286 )
Search Value (6, 9, 13): \(-0.633751051478\)
X1308
▸ Incident Central Lines11 lines
{1 840 36 105 100 514 101 513 103 517 104 516 106 1279 110 1019 813 876 901 1022 919 1027
▸ Functional Relations6 relations
