X357
1st MORLEY-TAYLOR-MARR CENTER
X357 is the perspector of Morley triangle and
ABC , and also the Hofstadter 1/3 point. See
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) { 356, 358 }: Central Line L(356, 358) { 1134, 3275 }: Central Line L(1134, 3275)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5670, 0.2245) X_356 = MORLEY CENTER (0.5727, 0.2361) X_1134 = 3rd MORLEY-TAYLOR-MARR CENTER (0.5584, 0.2154) X_3275 = PERSPECTOR OF TRIANGLES S1S2S3 AND J1J2J3 (0.6086, 0.2928) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.5757, 0.2422)
A
B
C
X358
X356
X1134
X3275
X357
(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) { 356, 358 }: Central Line L(356, 358) { 1134, 3275 }: Central Line L(1134, 3275)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5945, 0.1877) X_356 = MORLEY CENTER (0.6015, 0.2039) X_1134 = 3rd MORLEY-TAYLOR-MARR CENTER (0.5820, 0.1772) X_3275 = PERSPECTOR OF TRIANGLES S1S2S3 AND J1J2J3 (0.6467, 0.2755) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.6052, 0.2125)
A
B
C
X358
X356
X1134
X3275
X357
(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) { 356, 358 }: Central Line L(356, 358) { 1134, 3275 }: Central Line L(1134, 3275)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5794, 0.1896) X_356 = MORLEY CENTER (0.5853, 0.2061) X_1134 = 3rd MORLEY-TAYLOR-MARR CENTER (0.5689, 0.1789) X_3275 = PERSPECTOR OF TRIANGLES S1S2S3 AND J1J2J3 (0.6238, 0.2794) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.5885, 0.2148)
A
B
C
X358
X356
X1134
X3275
X357
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) { 356, 358 }: Central Line L(356, 358) { 1134, 3275 }: Central Line L(1134, 3275)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.6114, 0.1134) X_356 = MORLEY CENTER (0.6164, 0.1355) X_1134 = 3rd MORLEY-TAYLOR-MARR CENTER (0.5984, 0.1051) X_3275 = PERSPECTOR OF TRIANGLES S1S2S3 AND J1J2J3 (0.6500, 0.2099) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.6190, 0.1470)
A
B
C
X358
X356
X1134
X3275
X357
Kimberling (6, 9, 13) | AB = 1
X357 (1st MORLEY-TAYLOR-MARR CENTER ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(\sec A/3 : \sec B/3 : \sec C/3\)
Barycentrics: \(\sin A \sec A/3 : \sin B \sec B/3 : \sin C \sec C/3\)
Search Value (6, 9, 13): \(1.486625299299\)
▸ Incident Central Lines3 lines
{356 358 1134 3275 3280
▸ Functional Relations3 relations
Notes
F. Glanville Taylor and W. L. Marr, “The six trisectors of each of the angles of a triangle,” Proceedings of the Edinburgh Mathematical Society 33 (1913-14) 119-131, especially item 9, page 127.
