Κυριακή, 4 Νοεμβρίου 2018

NEW POINTS

X(28341) =  (name pending)

Barycentrics    2 a^22-9 a^20 (b^2+c^2)+4 a^18 (3 b^4+8 b^2 c^2+3 c^4)-(b^2-c^2)^8 (b^6+b^4 c^2+b^2 c^4+c^6)+a^16 (3 b^6-41 b^4 c^2-41 b^2 c^4+3 c^6)+a^14 (-20 b^8+28 b^6 c^2+74 b^4 c^4+28 b^2 c^6-20 c^8)+2 a^2 (b^2-c^2)^6 (2 b^8-b^6 c^2-b^2 c^6+2 c^8)+2 a^10 b^2 c^2 (11 b^8+3 b^6 c^2+26 b^4 c^4+3 b^2 c^6+11 c^8)-2 a^8 (b^2-c^2)^2 (b^10+3 b^8 c^2-6 b^6 c^4-6 b^4 c^6+3 b^2 c^8+c^10)-a^4 (b^2-c^2)^4 (5 b^10-17 b^8 c^2-b^6 c^4-b^4 c^6-17 b^2 c^8+5 c^10)+a^12 (14 b^10-24 b^8 c^2-71 b^6 c^4-71 b^4 c^6-24 b^2 c^8+14 c^10)+2 a^6 (b^2-c^2)^2 (b^12-10 b^10 c^2+b^8 c^4-6 b^6 c^6+b^4 c^8-10 b^2 c^10+c^12) : :
Barycentrics    R^2 S^4 + (-92 R^6-21 R^2 SB SC+99 R^4 SW+4 SB SC SW-35 R^2 SW^2+4 SW^3) S^2 + 132 R^6 SB SC-157 R^4 SB SC SW+63 R^2 SB SC SW^2-8 SB SC SW^3 : :

As a point on the Euler line, X(28341) has Shinagawa coefficients {92 R^6-99 R^4 SW-4 SW^3-R^2 (S^2-35 SW^2), -132 R^6+157 R^4 SW-4 S^2 SW+8 SW^3+21 R^2 (S^2-3 SW^2)}.

See Tran Quang Hung and Ercole Suppa, Hyacinthos 28654.

X(28341) lies on this line: {2,3}


X(28342) =  (name pending)

Barycentrics    2 a^22-11 a^20 (b^2+c^2)+23 a^18 (b^2+c^2)^2-(b^2-c^2)^8 (b^6+c^6)-a^16 (19 b^6+67 b^4 c^2+67 b^2 c^4+19 c^6)+a^14 (-6 b^8+28 b^6 c^2+62 b^4 c^4+28 b^2 c^6-6 c^8)+a^2 (b^2-c^2)^6 (5 b^8-3 b^6 c^2-5 b^4 c^4-3 b^2 c^6+5 c^8)-a^4 (b^2-c^2)^4 (9 b^10-11 b^8 c^2-7 b^6 c^4-7 b^4 c^6-11 b^2 c^8+9 c^10)+a^8 (b^2-c^2)^2 (12 b^10+13 b^8 c^2+29 b^6 c^4+29 b^4 c^6+13 b^2 c^8+12 c^10)+a^12 (28 b^10+18 b^8 c^2-13 b^6 c^4-13 b^4 c^6+18 b^2 c^8+28 c^10)+2 a^6 (b^2-c^2)^2 (2 b^12-5 b^10 c^2-6 b^6 c^6-5 b^2 c^10+2 c^12)-a^10 (28 b^12+7 b^10 c^2+13 b^8 c^4-24 b^6 c^6+13 b^4 c^8+7 b^2 c^10+28 c^12) : :
Barycentrics    (5 R^2-2 SW) S^4 + (-160 R^6-51 R^2 SB SC+164 R^4 SW+14 SB SC SW-55 R^2 SW^2+6 SW^3) S^2 + 192 R^6 SB SC - 212 R^4 SB SC SW+81 R^2 SB SC SW^2-10 SB SC SW^3 : :

As a point on the Euler line, X(28342) has Shinagawa coefficients {(5 R^2 - 2 SW) (32 R^4 - S^2 - 20 R^2 SW + 3 SW^2), -192 R^6 + 212 R^4 SW - 14 S^2 SW + 10 SW^3 + R^2 (51 S^2 - 81 SW^2)}.

See Tran Quang Hung and Ercole Suppa, Hyacinthos 28654.

X(28342) lies on this line: {2,3}


X(28343) =  MIDPOINT OF X(6) AND X(112)

Barycentrics    a^2 (a^4-b^4+b^2 c^2-c^4) (2 a^6-a^4 b^2-b^6-a^4 c^2+b^4 c^2+b^2 c^4-c^6) : :
X(28343) = X[127]-2*X[3589], X[141]-2*X[6720], X[1297]-3*X[5085], 5*X[3618]-X[13219], 3*X[5050]+X[13310], X[10749]-3*X[14561], 5*X[12017]-X[13115], X[12384]+3*X[25406], X[13200]+3*X[14853], X[13221]+3*X[16475], 3*X[16225]-X[19161], 2*X[19130]-X[19163]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28655.

X(28343) lies on these lines: {6,74}, {127,3589}, {132,1503}, {141,6720}, {518,11722}, {611,13312}, {613,13311}, {1297,5085}, {1384,14649}, {1428,3320}, {1691,13195}, {1974,13166}, {2330,6020}, {2492,6593}, {2794,5480}, {2799,5026}, {3618,13219}, {5039,14676}, {5050,13310}, {8744,18374}, {9019,10317}, {9142,21309}, {9157,17810}, {10749,14561}, {11610,14495}, {12017,13115}, {12145,19124}, {12384,25406}, {13200,14853}, {13221,16475}, {16225,19161}, {19130,19163}

X(28343) = midpoint of X(6) and X(112)
X(28343) = reflection of X(i) in X(j) for these {i,j}: {127,3589}, {141,6720}, {19163,19130}


X(28344) =  MIDPOINT OF X(7) AND X(934)

Barycentrics    (a+b-c) (a-b+c) (2 a^2-a b-b^2-a c+2 b c-c^2) (a^4 b-2 a^3 b^2+2 a b^4-b^5+a^4 c+2 a^3 b c-2 a b^3 c-b^4 c-2 a^3 c^2+2 b^3 c^2-2 a b c^3+2 b^2 c^3+2 a c^4-b c^4-c^5) : :
X(28344) = 2*X[142]-X[5514], X[972]-3*X[21151]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28655.

X(28344) lies on these lines: {7,104}, {142,5514}, {658,13257}, {971,1543}, {972,21151}, {1360,3323}, {3321,12831}, {4617,15252}, {6366,10427}

X(28344) = midpoint of X(7) and X(934)
X(28344) = reflection of X(5514) in X(142)


X(28345) =  MIDPOINT OF X(9) AND X(101)

Barycentrics    a (a^2-2 a b+b^2-2 a c+b c+c^2) (2 a^3-a^2 b-b^3-a^2 c+b^2 c+b c^2-c^3) : :
X(28295) = X[103]-3*X[21153], X[116]-2*X[6666], X[142]-2*X[6710], X[150]-5*X[18230]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28655.

X(28345) lies on these lines: {2,14154}, {9,48}, {103,21153}, {116,6666}, {118,516}, {142,6710}, {150,18230}, {518,11712}, {528,21090}, {954,11028}, {1001,2809}, {3022,15837}, {3887,6594}, {5375,16586}, {5526,15730}

X(28345) = midpoint of X(9) and X(101)
X(28345) = reflection of X(i) in X(j) for these {i,j}: {116,6666}, {142,6710}


X(28346) =  MIDPOINT OF X(10) AND X(101)

Barycentrics    (a^2+a b-b^2+a c-b c-c^2) (2 a^3-a^2 b-b^3-a^2 c+b^2 c+b c^2-c^3) : :
X(28346) = 3*X[2]+X[1282], X[103]-3*X[10164], X[116]-2*X[3634], X[150]-5*X[1698], X[152]+3*X[165], 3*X[551]-X[10695], 7*X[9780]+X[20096], 3*X[10175]-X[10739]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28655.

X(28346) lies on these lines: {2,1282}, {10,98}, {103,10164}, {116,3634}, {118,516}, {120,24685}, {150,1698}, {152,165}, {519,11712}, {544,3828}, {551,10695}, {1125,2809}, {1362,3911}, {2786,9508}, {2801,3035}, {2808,6684}, {2810,6686}, {3033,6685}, {3842,6690}, {4712,24582}, {6541,17927}, {9780,20096}, {10175,10739}, {11028,13405}, {13411,18413}, {14543,21914}

X(28346) = midpoint of X(10) and X(101)
X(28346) = reflection of X(i) in X(j) for these {i,j}: {116,3634}, {1125,6710}


X(28347) =  MIDPOINT OF X(11) AND (2720)

Barycentrics    (a^5-a^4 b-2 a^3 b^2+2 a^2 b^3+a b^4-b^5-a^4 c+5 a^3 b c-2 a^2 b^2 c-3 a b^3 c+b^4 c-2 a^3 c^2-2 a^2 b c^2+4 a b^2 c^2+2 a^2 c^3-3 a b c^3+a c^4+b c^4-c^5) (2 a^7-2 a^6 b-3 a^5 b^2+3 a^4 b^3+a b^6-b^7-2 a^6 c+8 a^5 b c-3 a^4 b^2 c-4 a^3 b^3 c+4 a^2 b^4 c-4 a b^5 c+b^6 c-3 a^5 c^2-3 a^4 b c^2+8 a^3 b^2 c^2-4 a^2 b^3 c^2-a b^4 c^2+3 b^5 c^2+3 a^4 c^3-4 a^3 b c^3-4 a^2 b^2 c^3+8 a b^3 c^3-3 b^4 c^3+4 a^2 b c^4-a b^2 c^4-3 b^3 c^4-4 a b c^5+3 b^2 c^5+a c^6+b c^6-c^7) : :
X(28347) = X[11]+X[2720], X[1737]+X[15524], X[2745]-3*X[21154]

See Antreas Hatzipolakis and Ercole Suppa, Hyacinthos 28655.

X(28347) lies on these lines: {11,2720}, {521,3035}, {522,10271}, {1737,15524}, {2745,21154}, {3660,6001}

X(28347) = midpoint of X(i) and X(j) for these {i,j}: {11,2720}, {1737,15524}



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