X(45168) = EULER LINE INTERCEPT OF X(52)X(323)
Barycentrics a^2 (a-b-c)^2 (a+b-c)^2 (a-b+c)^2 (a+b+c)^2 (a^4+5 a^2 b^2+b^4-2 a^2 c^2-2 b^2 c^2+c^4) (a^8-2 a^6 b^2+2 a^2 b^6-b^8-2 a^6 c^2+3 a^4 b^2 c^2-4 a^2 b^4 c^2+3 b^6 c^2-4 a^2 b^2 c^4-4 b^4 c^4+2 a^2 c^6+3 b^2 c^6-c^8) : :Barycentrics (SB+SC) (S^2-8 R^2 SA+SA^2-4 SB SC) (3 S^2+7 SC^2) : :
X(45168) = X(3)+3*X(13621),2*X(3)+3*X(34484),X(3)-3*X(43809),X(34484)+2*X(43809)
As a point on the Euler line, X(45168) has Shinagawa coefficients (E-4*F,2*E+4*F).
See Antreas Hatzipolakis and Ercole Suppa, Euclid 2688 .
X(45168) lies on these lines: {2,3}, {6,9545}, {32,15355}, {49,1199}, {51,34148}, {52,323}, {54,5462}, {96,11815}, {110,389}, {143,22115}, {156,15032}, {161,18928}, {182,15028}, {184,15043}, {185,15053}, {195,16881}, {390,10046}, {511,43811}, {567,15026}, {569,11464}, {575,6467}, {578,5640}, {1092,3060}, {1125,9590}, {1147,1994}, {1173,5504}, {1181,35264}, {1204,15305}, {1493,11597}, {1495,9729}, {1511,10095}, {1588,9682}, {1614,9730}, {2079,7745}, {2393,43815}, {2888,3580}, {2917,37649}, {2929,13568}, {2931,9820}, {3043,16222}, {3047,20771}, {3066,11425}, {3284,8882}, {3292,15801}, {3357,11439}, {3410,12359}, {3448,12134}, {3574,5972}, {3581,11591}, {3600,10037}, {3618,15577}, {3620,37488}, {3815,44523}, {4993,19185}, {5012,10282}, {5254,44537}, {5286,44527}, {5422,19357}, {5446,38848}, {5449,41171}, {5609,11561}, {5622,43130}, {5651,11444}, {5731,8185}, {5866,32819}, {5889,9306}, {5890,10539}, {5907,43614}, {5926,10280}, {5943,13367}, {5944,13353}, {6000,43601}, {6102,18350}, {6146,43816}, {6193,37644}, {6403,8538}, {6684,9625}, {6696,10117}, {6699,18488}, {6759,10574}, {6800,37514}, {7585,8276}, {7586,8277}, {7592,9544}, {7689,15058}, {7691,11793}, {7735,9608}, {7738,44524}, {7999,37478}, {8907,11427}, {9538,11399}, {9541,35777}, {9591,10164}, {9626,10165}, {9659,10588}, {9672,10589}, {9706,13366}, {9707,11003}, {9713,30478}, {9723,32835}, {9780,15177}, {9781,13352}, {9786,11441}, {9833,18911}, {9924,15582}, {10314,26216}, {10316,10986}, {10540,13630}, {10541,35707}, {10545,11430}, {10546,11438}, {10601,17821}, {10610,32205}, {10982,38942}, {10984,26881}, {10985,22401}, {11002,36747}, {11004,37493}, {11064,11745}, {11202,11451}, {11264,23236}, {11440,15030}, {11468,16261}, {11477,20806}, {11562,14094}, {12038,15033}, {12112,13491}, {12278,18390}, {12282,41619}, {12300,12358}, {12370,12383}, {12584,22330}, {13142,22550}, {13289,15059}, {13346,34417}, {13347,35268}, {13364,43394}, {13392,22051}, {13445,13474}, {13472,15317}, {13567,14516}, {13598,44106}, {13754,43598}, {14061,39854}, {14157,40647}, {14627,32609}, {14652,34837}, {14671,14675}, {14683,18932}, {14915,43804}, {15019,37505}, {15045,26882}, {15049,43610}, {15054,21650}, {15062,21663}, {15066,17834}, {15068,37490}, {15072,26883}, {15080,37515}, {15107,15644}, {15139,41589}, {15531,44489}, {15647,32184}, {16194,43604}, {17701,41671}, {17704,32237}, {17810,35602}, {18381,26913}, {18474,26917}, {18475,43651}, {18912,34799}, {18931,40914}, {19459,33748}, {20190,43129}, {20304,22804}, {20791,44082}, {20987,25406}, {22800,34563}, {22948,44573}, {25739,43817}, {30482,30504}, {30522,43821}, {31834,32608}, {33884,37486}, {34782,37648}, {34835,40604}
X(45168) = midpoint of X(13621) and X(43809)
X(45168) = reflection of X(34484) in X(13621)
X(45168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,24,7488), (2,7487,37444), (2,7488,37126), (2,31304,6643), (3,4,12086), (3,5,35500), (3,378,35494), (3,546,14865), (3,1995,3091), (3,3091,7527), (3,3518,23), (3,3525,7496), (3,3627,7464), (3,3628,7550), (3,7506,13861), (3,7530,3529), (3,7545,3627), (3,10594,3146), (3,12086,2071), (3,12088,16661), (3,12106,3518), (3,13861,4), (3,18369,546), (3,31861,35475), (3,35494,35497), (3,35500,14118), (3,37440,12088), (3,37924,12103), (4,631,44441), (4,3548,31074), (4,6644,22467), (4,7506,13595), (4,22467,2071), (5,186,14118), (5,10018,2), (5,16532,140), (5,34330,1656), (5,38321,4), (5,44211,10018), (23,16661,12088), (24,6642,2), (24,7488,37940), (24,7509,14070), (24,10018,186), (25,17928,20), (26,631,6636), (49,5946,1199), (54,5462,34545), (110,16223,40640), (140,2070,7512), (140,7512,15246), (140,13163,33332), (156,37481,15032), (186,14118,38448), (186,35500,3), (376,7517,12087), (378,7529,3832), (381,37814,3520), (403,31833,34007), (468,9825,13160), (550,18378,37925), (569,15024,15018), (631,35482,23336), (632,12107,3), (1147,3567,1994), (1511,10095,37472), (1594,16238,2), (1598,11413,3543), (1656,1658,35921), (2070,16532,186), (2072,31830,4), (3146,14002,10594), (3147,7401,2), (3147,14940,10018), (3292,16625,15801), (3515,5020,7503), (3515,7503,10298), (3518,12088,37440), (3520,37814,37941), (3525,7556,3), (3530,37936,13564), (3545,21844,7526), (3546,37122,7391), (3627,7545,26863), (3628,7575,3), (3843,11250,13596), (3850,15646,14130), (5004,5005,7667), (5020,7503,5056), (5056,10298,7503), (5576,44452,6143), (5640,11449,578), (5890,10539,43605), (5943,13367,13434), (5944,13363,13353), (6636,44441,2071),(6644,7506,4),(6644,13595,2071),(6644,13861,3),(6644,38321,186),(7464,26863,3627),(7528,37119,5169),(7542,10127,14788),(7542,14788,2), (7542,44234,10018), (7555,14869,3), (7667,40132,7570), (9707,36752,11003), (9714,10323,37913), (9786,35259,11441), (10024,44232,37943), (10303,38435,3), (10546,11438,15052), (11464,15024,569), (12086,22467,3), (12088,37440,23), (12134,26879,3448), (13595,22467,4), (14130,21308,3850), (14157,43597,40647), (15026,32171,567), (15717,37913,10323), (16881,40111,195), (21451,34007,403), (22462,34864,547), (22462,37922,34864), (26863,35500,18403), (37126,37940,7488), (38848,43574,5446)
X(45178) = EULER LINE INTERCEPT OF X(113)X(11817)
Barycentrics (a-b-c)^2 (a+b-c)^2 (a-b+c)^2 (a+b+c)^2 (a^2+b^2-c^2) (a^2-b^2+c^2) (a^4+5 a^2 b^2+b^4-2 a^2 c^2-2 b^2 c^2+c^4) (a^4 b^2-2 a^2 b^4+b^6+a^4 c^2+10 a^2 b^2 c^2-b^4 c^2-2 a^2 c^4-b^2 c^4+c^6) : :Barycentrics SB SC (3 S^2+7 SC^2) (14 R^2-SA-SW) : :
X(45178) = X(1657)-5*X(43809),3*X(3830)+5*X(13621)
As a point on the Euler line, X(45178) has Shinagawa coefficients (-2*F,5*E-2*F).
See Antreas Hatzipolakis and Ercole Suppa, Euclid 2688 .
X(45178) lies on these lines: {2,3}, {113,11817}, {133,11792}, {389,32111}, {1503,43812}, {1514,11745}, {1533,9729}, {1614,16657}, {2883,3567}, {5254,33885}, {5890,15873}, {6152,22970}, {11381,26879}, {11439,12359}, {11457,15811}, {12022,26883}, {12112,18914}, {12241,14157}, {12290,13567}, {12300,41598}, {13366,14862}, {13568,38848}, {15033,16252}, {15063,16625}, {15305,41587}, {16621,25739}, {16659,18390}, {22660,36852}, {22802,34417}, {33880,39565}
X(45178) = midpoint of X(4) and X(34484)
X(45178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,25,18560), (4,186,13488), (4,235,1594), (4,403,15559), (4,1598,7576), (4,3089,378), (4,3518,1885), (4,3542,35502), (4,6623,7547), (4,7487,35490), (4,7505,1597), (4,7577,1907), (4,10594,6240), (4,16868,1595), (4,26863,6756), (4,37119,11403), (4,37122,35480), (235,1594,403), (235,1595,16868), (428,44226,4), (546,11799,13160), (1595,16868,1594), (1596,1906,4), (1885,3518,10295), (3542,35502,37118), (3843,15761,5133), (3861,11563,5576), (7487,35490,6240), (10594,35490,7487), (11403,37119,35484), (13861,31725,38323), (18535,37197,4)
X(45181) = EULER LINE INTERCEPT OF X(11)X(4351)
Barycentrics (a^2-b^2-c^2) (a^2+b^2-c^2) (a^2-b^2+c^2) (a^8 b^2-2 a^6 b^4+2 a^2 b^8-b^10+a^8 c^2+6 a^6 b^2 c^2-2 a^4 b^4 c^2-8 a^2 b^6 c^2+3 b^8 c^2-2 a^6 c^4-2 a^4 b^2 c^4+12 a^2 b^4 c^4-2 b^6 c^4-8 a^2 b^2 c^6-2 b^4 c^6+2 a^2 c^8+3 b^2 c^8-c^10) (a^10+2 a^8 b^2-3 a^6 b^4-3 a^4 b^6+2 a^2 b^8+b^10-3 a^8 c^2-3 a^6 b^2 c^2+8 a^4 b^4 c^2-3 a^2 b^6 c^2-3 b^8 c^2+2 a^6 c^4-3 a^4 b^2 c^4-3 a^2 b^4 c^4+2 b^6 c^4+2 a^4 c^6+7 a^2 b^2 c^6+2 b^4 c^6-3 a^2 c^8-3 b^2 c^8+c^10) : :Barycentrics (SC^2 (18 R^2-5 SW)+S^2 (6 R^2-SW)) (S^2 (3 R^2-SW)+SB SC (9 R^2-SW)) : :
X(45181) = 2*X(3)-3*X(44214),3*X(4)-X(10296),X(4)+2*X(16619),2*X(5)-3*X(403),4*X(5)-3*X(2072),X(5)-3*X(11563),5*X(5)-3*X(37938),X(5)+3*X(43893),X(20)-3*X(186),X(20)-5*X(37760),2*X(20)-3*X(44246),3*X(23)+X(10296),2*X(23)+X(18323),2*X(140)-3*X(44282),3*X(186)-5*X(37760),X(376)-3*X(37907),3*X(376)-5*X(37952),3*X(381)-X(7574),3*X(381)-2*X(10297),3*X(381)+X(37924),3*X(381)-4*X(37984),X(382)+3*X(2070),X(382)-3*X(31726),X(382)+4*X(37897),X(382)+6*X(37971),3*X(403)-X(858),5*X(403)-2*X(37938),X(403)+2*X(43893),2*X(468)+X(18325),4*X(468)-3*X(44214),4*X(546)+X(37900),2*X(546)+X(37967),X(548)-3*X(10096),2*X(548)-3*X(15646),4*X(548)-3*X(16386),2*X(550)-3*X(44280),5*X(631)-3*X(2071),5*X(631)-9*X(37943),5*X(631)-6*X(44452),X(691)-3*X(38227),2*X(858)-3*X(2072),X(858)-6*X(11563),5*X(858)-6*X(37938),X(858)+6*X(43893),2*X(1514)+X(3581),5*X(1656)-4*X(5159),5*X(1656)-X(35001),X(1657)-4*X(37934),X(1657)-5*X(37958),3*X(2070)-4*X(37897),X(2071)-3*X(37943),X(2072)-4*X(11563),5*X(2072)-4*X(37938),X(2072)+4*X(43893),7*X(3090)-5*X(30745),5*X(3091)-X(5189),5*X(3091)+X(37946),X(3146)+5*X(37953),3*X(3153)-7*X(3832),3*X(3153)+X(20063),7*X(3526)-6*X(10257),7*X(3526)-3*X(18859),7*X(3526)-8*X(37911),7*X(3528)-9*X(37941),X(3529)-7*X(37957),4*X(3530)-3*X(34152),2*X(3530)-3*X(44234),X(3543)+3*X(37909),3*X(3545)-X(10989),X(3627)+2*X(12105),X(3830)+2*X(37904),3*X(3830)+5*X(37923),7*X(3832)+X(20063),7*X(3832)-6*X(23323),7*X(3832)+3*X(37925),3*X(3839)+X(37901),5*X(3843)+3*X(5899),5*X(3843)-6*X(10151),5*X(3843)-3*X(18403),5*X(3843)+2*X(37899),X(3853)-3*X(11558),2*X(3853)+3*X(37936),2*X(3853)-3*X(44283),4*X(3861)+3*X(37947),4*X(5159)-X(35001),X(5899)+2*X(10151),3*X(5899)-2*X(37899),3*X(7426)-2*X(7575),3*X(7426)-X(10295),3*X(7426)-4*X(25338),9*X(7426)-8*X(44264),3*X(7426)+2*X(44267),X(7574)-4*X(37984),3*X(7575)-4*X(44264),4*X(7575)-3*X(44265),X(7575)-3*X(44266),X(7728)+2*X(32269),4*X(10096)-X(16386),3*X(10096)-2*X(22249),3*X(10151)+X(37899),3*X(10257)-4*X(37911),X(10295)-4*X(25338),3*X(10295)-8*X(44264),2*X(10295)-3*X(44265),X(10295)-6*X(44266),X(10295)+2*X(44267),X(10296)+6*X(16619),2*X(10296)-3*X(18323),2*X(10297)+X(37924),3*X(10540)-X(23236),2*X(11064)-3*X(14643),2*X(11558)+X(37936),5*X(11563)-X(37938),X(12121)-4*X(15448),X(12295)+2*X(32237),X(12383)-3*X(35265),3*X(13445)-7*X(15057),2*X(13473)+3*X(37956),3*X(13619)+X(33703),X(13619)-3*X(37940),3*X(14643)-X(37477),3*X(15362)-X(20126),3*X(15362)-2*X(44569),3*X(15646)-4*X(22249),5*X(15696)-9*X(37955),3*X(16222)-4*X(44084),6*X(16227)-5*X(37481),3*X(16386)-8*X(22249),4*X(16531)-3*X(37941),3*X(16532)-2*X(37968),4*X(16619)+X(18323),5*X(17578)+9*X(37939),X(17800)-9*X(37922),X(17800)-6*X(37931),2*X(18325)+3*X(44214),3*X(18374)-X(32233),3*X(18403)+2*X(37899),4*X(18571)-3*X(44280),2*X(18572)+X(37900),2*X(18579)-3*X(37907),6*X(18579)-5*X(37952),3*X(18859)-8*X(37911),X(18859)-4*X(37942),X(20063)+6*X(23323),X(20063)-3*X(37925),2*X(20725)-3*X(38788),2*X(23323)+X(37925),3*X(25338)-2*X(44264),8*X(25338)-3*X(44265),2*X(25338)-3*X(44266),2*X(25338)+X(44267),3*X(31726)+4*X(37897),X(31726)+2*X(37971),X(33703)+9*X(37940),10*X(37760)-3*X(44246),2*X(37897)-3*X(37971),6*X(37904)-5*X(37923),9*X(37907)-5*X(37952),2*X(37911)-3*X(37942),3*X(37922)-2*X(37931),X(37924)+4*X(37984),4*X(37934)-5*X(37958),4*X(37935)-3*X(37955),X(37938)+5*X(43893),3*X(37943)-2*X(44452),X(37950)-3*X(44282),4*X(44264)-9*X(44266),4*X(44264)+3*X(44267),X(44265)-4*X(44266),3*X(44265)+4*X(44267),3*X(44266)+X(44267)
As a point on the Euler line, X(45181) has Shinagawa coefficients (E+4*F,-5*E+4*F).
See Antreas Hatzipolakis and Ercole Suppa, Euclid 2688 .
X(45181) lies on these lines: {2,3}, {11,4351}, {12,4354}, {49,16252}, {94,10688}, {113,511}, {115,3003}, {125,1533}, {127,18809}, {133,38971}, {195,13142}, {265,1177}, {339,44138}, {343,18435}, {399,3564}, {495,9642}, {517,41607}, {523,19912}, {524,5655}, {541,32225}, {567,16657}, {691,38227}, {1154,41596}, {1495,17702}, {1498,25738}, {1499,36255}, {1514,3581}, {1614,12370}, {2393,15125}, {2777,32110}, {2781,8262}, {2883,34783}, {3292,16534}, {3448,12112}, {3521,13568}, {3580,5663}, {3767,16306}, {5063,5475}, {5139,42424}, {5254,16308}, {5446,43831}, {5449,11381}, {5480,8705}, {5486,20423}, {5511,42422}, {5512,16188}, {5656,18917}, {5891,40107}, {5965,6053}, {5972,10564}, {6000,16003}, {6243,22660}, {6530,34334}, {6759,44076}, {6795,16324}, {7687,29012}, {7706,34417}, {8758,11809}, {9644,37719}, {9704,43595}, {9820,37495}, {9927,26883}, {10112,14862}, {10149,15888}, {10293,15362}, {10540,23236}, {10610,15807}, {10706,15360}, {10752,41721}, {11064,14643}, {11455,23293}, {11472,37638}, {11645,20301}, {11649,18388}, {12121,15448}, {12188,38595}, {12279,26917}, {12295,32237}, {12359,18439}, {12383,35265}, {12420,12429}, {12897,13367}, {12918,20957}, {13394,14805}, {13445,15057}, {13470,43865}, {13491,26879}, {13556,38953}, {13754,14448}, {13851,44407}, {14094,41724}, {14672,42426}, {14693,38611}, {14934,16319}, {15060,37636}, {15069,18451}, {15305,38397}, {16194,21243}, {16222,44084}, {16227,37481}, {16658,34514}, {16760,18860}, {18374,32233}, {18445,34117}, {18474,44470}, {18914,22533}, {20725,38788}, {24855,40115}, {29181,32218}, {32137,34826}, {32358,43605}, {34150,40352}, {36982,41725}, {37648,40280}, {38577,38583}, {39899,41719}
X(45181) = midpoint of X(i) and X(j) for these {i,j}: {3,18325}, {4,23}, {125,1533}, {1514,32269}, {2070,31726}, {3153,37925}, {3448,12112}, {3580,32111}, {3581,7728}, {5189,37946}, {5899,18403}, {7574,37924}, {7575,44267}, {10706,15360}, {10752,41721}, {11563,43893}, {11676,36174}, {14094,41724}, {15063,41586}, {18572,37967}, {37936,44283}
X(45181) = reflection of X(i) in X(j) for these (i,j): (3,468), (23,16619), (376,18579), (403,11563), (548,22249), (550,18571), (858,5), (2070,37971), (2071,44452), (2072,403), (3153,23323), (3292,16534), (3581,32269), (6795,16324), (7426,44266), (7464,15122), (7472,37459), (7574,10297), (7575,25338), (7728,1514), (10257,37942), (10295,7575), (10297,37984), (10564,5972), (14934,16319), (15646,10096), (15980,14120), (16386,15646), (18323,4), (18403,10151), (18572,546), (18859,10257), (18860,16760), (20126,44569), (32110,32223), (34152,44234), (37477,11064), (37900,37967), (37950,140), (38611,14693), (44246,186), (44265,7426), (44283,11558)
X(45181) = reflection of X(2) in X(523)X(44204)
X(45181) = complement of X(7464)
X(45181) = anticomplement of X(15122)
+
X(45181) = complementary conjugate of the complement of X(10293)
X(45181) = circumperp conjugate of the ctic conjugate of X(40914)
X(45181) = X(5475)-line conjugate of X(5063)
X(45181) = X(523)-vertex conjugate of X(6644)
X(45181) = crossdifference of every pair of points on line X(647)-X(5063)
X(45181) = crosssum of X(i)and X(j) for these {i,j}: {3,15136},{6,40114}
X(45181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,4,31861), (2,7464,15122), (2,13596,44236), (3,468,44214), (3,5073,34622), (3,5899,37928), (3,37973,2070), (4,26,18563), (4,403,37981), (4,7530,7540), (4,7552,7527), (4,10024,5576), (4,15761,10024), (5,20,37452), (5,427,7579), (5,858,2072), (5,1906,3843), (5,3853,15559), (20,37760,186), (23,186,26), (23,11563,10024), (186,3542,468), (235,468,403), (235,43893,18325), (376,37907,18579), (381,7574,10297), (381,12083,18531), (381,15154,10751), (381,15155,10750), (381,15760,37347), (381,18534,31723), (381,37924,7574), (403,858,5), (403,18323,5576), (468,1885,44281), (546,7553,31724), (546,16618,34664), (548,10096,22249), (548,22249,15646), (550,18571,44280), (1113,1114,6644), (1312,1313,381), (1346,1347,39484), (1596,15760,381), (1658,44271,18560), (1885,13383,3), (2041,2042,12084), (2070,7517,23), (2071,37943,44452), (2072,37981,5576), (2883,41587,34783), (3091,14789,5), (3146,16868,13371), (3627,13406,1594), (3830,10254,427), (3832,20063,3153), (5073,10255,23335), (5169,7493,30739), (5189,37943,13154), (6623,18531,381), (7387,37197,18404), (7426,10295,7575), (7527,7552,140), (7542,13488,14130), (7575,10295,44265), (7575,25338,7426), (7575,44266,25338), (7579,10254,5), (10024,18323,2072), (10096,16238,468), (10201,44276,378), (10257,37911,3526), (10297,37984,381), (10750,10751,31723), (12086,14940,23336), (13160,18572,2072), (14120,36169,381), (14643,37477,11064), (15154,15155,18534), (15362,20126,44569), (15761,43893,23), (16618,34664,3), (18323,44246,18563), (18325,31726,31725), (20408,20409,382), (25338,44267,10295), (34007,34484,31830), (37440,44279,6240), (37950,44282,140), (44266,44267,7575)
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου