X3334
PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3
The equilateral triangles
T1 T2 T3 and
J1 J2 J3 are defined just before
X3272 . The points
X3334 and
X3335 , contributed April 16, 2008 by
Peter Moses , complete a list (just before
X3272 of perspectors associated with equilateral triangles.
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) { 3, 3272 }: Central Line L(3, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5670, 0.2245) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5698, 0.2349) X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3 (0.5478, 0.1930)
A
B
C
X16
X358
X3
X3272
X3334
(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) { 3, 3272 }: Central Line L(3, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_16 = 2nd ISODYNAMIC POINT (1.3303, 1.4234) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5945, 0.1877) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5970, 0.2039) X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3 (0.5688, 0.1446)
A
B
C
X16
X358
X3
X3272
X3334
(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) { 3, 3272 }: Central Line L(3, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_16 = 2nd ISODYNAMIC POINT (1.2449, 1.5332) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5794, 0.1896) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5815, 0.2061) X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3 (0.5577, 0.1458)
A
B
C
X16
X358
X3
X3272
X3334
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) { 3, 3272 }: Central Line L(3, 3272)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_16 = 2nd ISODYNAMIC POINT (0.8687, 0.7568) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.6114, 0.1134) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.6112, 0.1398) X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3 (0.5893, 0.0580)
A
B
C
X16
X358
X3
X3272
X3334
Kimberling (6, 9, 13) | AB = 1
X3334 (PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(\cos A + 2 \sin(B/3) \sin(C/3) + \sin(A/3 +\pi /6) : :\)
Search Value (6, 9, 13): \(2.640439099336\)
▸ Incident Central Lines5 lines
{3 3272 16 358 357 1134 1136
▸ Functional Relations1 relation
