Τρίτη, 10 Δεκεμβρίου 2019

NEW POINTS

X(36837) =  EULER LINE INTERCEPT OF X(1141)X(6343)

Barycentrics    2*a^16-5*a^14*b^2-5*a^12*b^4+31*a^10*b^6-45*a^8*b^8+33*a^6*b^10-15*a^4*b^12+5*a^2*b^14-b^16-5*a^14*c^2-2*a^12*b^2*c^2+31*a^10*b^4*c^2-24*a^8*b^6*c^2-27*a^6*b^8*c^2+50*a^4*b^10*c^2-31*a^2*b^12*c^2+8*b^14*c^2-5*a^12*c^4+31*a^10*b^2*c^4-12*a^8*b^4*c^4-15*a^6*b^6*c^4-34*a^4*b^8*c^4+63*a^2*b^10*c^4-28*b^12*c^4+31*a^10*c^6-24*a^8*b^2*c^6-15*a^6*b^4*c^6-2*a^4*b^6*c^6-37*a^2*b^8*c^6+56*b^10*c^6-45*a^8*c^8-27*a^6*b^2*c^8-34*a^4*b^4*c^8-37*a^2*b^6*c^8-70*b^8*c^8+33*a^6*c^10+50*a^4*b^2*c^10+63*a^2*b^4*c^10+56*b^6*c^10-15*a^4*c^12-31*a^2*b^2*c^12-28*b^4*c^12+5*a^2*c^14+8*b^2*c^14-c^16 : :
Barycentrics    4 S^4+S^2 (57 R^4+4 SB SC-44 R^2 SW+8 SW^2)-SB SC (43 R^4-36 R^2 SW+8 SW^2) ::
X(36837) = 3*X(3)+X(28237), 3*X(5)-4*X(13469), 3*X(5)-2*X(15335), 3*X(547)-4*X(12056), 3*X(549)-X(10205), 3*X(549)-2*X(15334), 5*X(632)-4*X(12057),7*X(3090)-8*X(34420), 3*X(8703)-2*X(15336), X(10126)-4*X(15327), 3*X(10285)-X(28237), 3*X(11539)-2*X(15333), 4*X(13469)+3*X(14142),3*X(14142)+2*X(15335), 4*X(16239)-3*X(34479)

As a point on the Euler line, X(36837) has Shinagawa coefficients (57 R^4 - 44 R^2 SW + 4 (S^2 + 2 SW^2),-43 R^4 + 36 R^2 SW + 4 (S^2 - 2 SW^2)).

See Tran Quang Hung and Ercole Suppa, Euclid 655 .

X(36837) lies on these lines: {2,3}, {54,24385}, {1141,6343}, {1263,25042}, {8254,16337}, {10610,12026}, {14140,34804}, {31879,34598}, {32423,32551}, {32744,33545}

X(36837) = midpoint of X(i) and X(j) for these {i,j}: {3,10285}, {5,14142}, {550,20120}
X(36837) = reflection of X(i) in X(j) for these (i,j): (4,19940), (140,15327), (546,15957), (3853,25404), (5066,25403), (10126,140), (10205,15334), (15335,13469), (20030,5501), (27868,10289), (31879,34598)
X(36837) = anticomplement of X(10289)
X(36837) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,27868,10289), (549,10205,15334), (13469,15335,5)



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