X3273
PERSPECTOR OF TRIANGLES M1M2M3 AND J1J2J3
X3273 is the perspector of triangles m1m2m3 and j1j2j3.
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) { 16, 358 }: Central Line L(16, 358) { 357, 1136 }: Central Line L(357, 1136) { 356, 3272 }: Central Line L(356, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3604 = ISOGONAL CONJUGATE OF X(3273) (0.5684, 0.2299) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5670, 0.2245) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.5757, 0.2422) X_1136 = 5th MORLEY-TAYLOR-MARR CENTER (0.6158, 0.4039) X_356 = MORLEY CENTER (0.5727, 0.2361) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5698, 0.2349) X_3273 = PERSPECTOR OF TRIANGLES M1M2M3 AND J1J2J3 (0.5744, 0.2367)
A
B
C
X3604
X16
X358
X357
X1136
X356
X3272
X3273
(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) { 16, 358 }: Central Line L(16, 358) { 357, 1136 }: Central Line L(357, 1136) { 356, 3272 }: Central Line L(356, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_3604 = ISOGONAL CONJUGATE OF X(3273) (0.5958, 0.1960) X_16 = 2nd ISODYNAMIC POINT (1.3303, 1.4234) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5945, 0.1877) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.6052, 0.2125) X_1136 = 5th MORLEY-TAYLOR-MARR CENTER (0.6400, 0.4800) X_356 = MORLEY CENTER (0.6015, 0.2039) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5970, 0.2039) X_3273 = PERSPECTOR OF TRIANGLES M1M2M3 AND J1J2J3 (0.6041, 0.2040)
A
B
C
X3604
X16
X358
X357
X1136
X356
X3272
X3273
(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) { 16, 358 }: Central Line L(16, 358) { 357, 1136 }: Central Line L(357, 1136) { 356, 3272 }: Central Line L(356, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_3604 = ISOGONAL CONJUGATE OF X(3273) (0.5805, 0.1981) X_16 = 2nd ISODYNAMIC POINT (1.2449, 1.5332) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5794, 0.1896) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.5885, 0.2148) X_1136 = 5th MORLEY-TAYLOR-MARR CENTER (0.6180, 0.4859) X_356 = MORLEY CENTER (0.5853, 0.2061) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5815, 0.2061) X_3273 = PERSPECTOR OF TRIANGLES M1M2M3 AND J1J2J3 (0.5876, 0.2061)
A
B
C
X3604
X16
X358
X357
X1136
X356
X3272
X3273
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) { 16, 358 }: Central Line L(16, 358) { 357, 1136 }: Central Line L(357, 1136) { 356, 3272 }: Central Line L(356, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_3604 = ISOGONAL CONJUGATE OF X(3273) (0.6113, 0.1269) X_16 = 2nd ISODYNAMIC POINT (0.8687, 0.7568) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.6114, 0.1134) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.6190, 0.1470) X_1136 = 5th MORLEY-TAYLOR-MARR CENTER (0.6073, 0.6791) X_356 = MORLEY CENTER (0.6164, 0.1355) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.6112, 0.1398) X_3273 = PERSPECTOR OF TRIANGLES M1M2M3 AND J1J2J3 (0.6193, 0.1331)
A
B
C
X3604
X16
X358
X357
X1136
X356
X3272
X3273
Kimberling (6, 9, 13) | AB = 1
X3273 (PERSPECTOR OF TRIANGLES M1M2M3 AND J1J2J3 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(\sin(A/3 + \pi /3) : :\)
Search Value (6, 9, 13): \(1.627111702456\)
▸ Incident Central Lines3 lines
▸ Functional Relations3 relations
Notes
Let A'B'C' be the 1st Morley triangle. Let La be the line through A' parallel to BC , and define Lb and Lc cyclically. Let A″ = Lb ∩Lc , B″ = Lc ∩La , C″ = La ∩Lb . The lines AA″ , BB″ , CC″ concur in X3273 Randy Hutson , July 20, 2016)
