HYACINTHOS 28400

[Ercole Suppa]:

 

 

= MIDPOINT OF X(20) AND X(100) 

 

Barycentrics -4 a^7+4 a^6 (b+c)-a (b-c)^4 (b+c)^2+(b-c)^4 (b+c)^3+a^5 (7 b^2-10 b c+7 c^2)-a^4 (7 b^3+b^2 c+b c^2+7 c^3)-2 a^3 (b^4-4 b^3 c+2 b^2 c^2-4 b c^3+c^4) +2 a^2 (b^5-b^4 c-b c^4+c^5) : :

 

=3*X[2]-X[10724], 2*X[3]-X[11], X[4]-2*X[3035], X[20]+X[100], X[80]-3*X[165], X[104]-3*X[376], 2*X[140]-X[22938], X[149]-5*X[3522], 5*X[631]-4*X[6667], X[1320]-3*X[5731], 2*X[1387]-3*X[3576], X[1484]-3*X[8703], X[1657]+X[10742], 2*X[3036]-3*X[5657], X[3146]-4*X[20400], X[3529]+X[10728], X[4316]+X[5537], X[5538]+X[15228], X[6224]+3*X[9778], X[6246]-2*X[6684], X[6361]+X[10698], 2*X[6702]-3*X[10164], X[7957]+X[17660], X[7972]+X[7991], X[7982]-2*X[12735], 5*X[7987]-3*X[16173], X[9803]+X[9963], 3*X[10165]-2*X[16174], 3*X[10167]-2*X[15528], 2*X[10265]-X[12690], 3*X[10304]-X[10707], X[10711]+X[11001], X[10767]-3*X[15035], X[10768]-3*X[21166], X[10778]-3*X[15055], X[11698]+X[15704], 2*X[11729]-X[12699], X[12248]-5*X[17538], X[12773]-5*X[15696], X[13268]-3*X[16190], 2*X[14740]-X[14872]

 

= lies on these lines: {2,10724},{3,11},{4,3035},{20,100},{30,119},{40,550},{55,6948},{80,165},{104,376},{120,7427},{140,22938},{149,3522},{214,516},{411,17100},{515,1145},{517,1317},{548,11012},{631,6667},{944,5854},{971,6068},{1001,6955},{1155,12743},{1320,5731},{1350,5848},{1376,6938},{1387,3576},{1484,8703},{1657,10742},{1753,1862},{2771,16111},{2800,10609},{2802,4297},{2803,3184},{2806,14689},{2886,6950},{2932,7580},{2950,10860},{2951,6282},{3036,5657},{3058,10269},{3146,20400},{3529,10728},{3534,6244},{3925,6914},{4188,7681},{4190,11496},{4299,10087},{4304,12736},{4314,18240},{4316,5537},{4333,5812},{4413,6930},{4421,12115},{4880,5844},{4996,5842},{5010,6907},{5204,13274},{5217,6850},{5326,6980},{5432,6923},{5434,10679},{5533,7280},{5538,15228},{5732,5856},{5759,5851},{6200,13913},{6224,9778},{6246,6684},{6361,10698},{6690,6951},{6702,10164},{6827,12764},{6891,12953},{6921,10893},{6925,12761},{6934,12775},{6961,10896},{7354,10956},{7680,17579},{7957,17660},{7972,7991},{7982,12735},{7987,16173},{8227,17563},{8674,16163},{8735,22055},{9541,19082},{9803,9963},{10074,22770},{10165,16174},{10167,15528},{10265,12690},{10304,10707},{10711,11001},{10767,15035},{10768,21166},{10778,15055},{11698,15704},{11729,12699},{11849,15888},{12116,13271},{12248,17538},{12773,15696},{13268,16190},{14740,14872}

 

= midpoint of X(i) and X(j) for these {i,j}: {20,100},{40,12119},{104,13199},{1657,10742},{3529,10728},{4316,5537},{5538,15228},{6361,10698},{7957,17660},{7972,7991},{9803,9963},{10711,11001},{11698,15704}

 

= reflection of X(i) in X(j) for these {i,j}: {4,3035},{11,3},{149,20418},{1537,214},{6154,10993},{6246,6684},{6326,9945},{7982,12735},{10738,6713},{12690,10265},{12699,11729},{14217,1387},{14872,14740},{22938,140}

 

= {X(i),X(j)}-harmonic conjugate of X(k) for these {i,j,k}: {3,11,21154},{3,10525,5433},{3,10738,6713},{3,11826,15908},{20,10310,11827},{376,13199,104},{1155,12743,12832},{3576,14217,1387},{5010,6907,21155},{6713,10738,11}

 

Ercole Suppa