is the point on the line 
such that 
. It can also be thought of as the point of intersection
of two parallel lines. In 1639, Desargues (1864) became
the first to consider the point at infinity (Cremona 1960, p. ix), although
Poncelet was the first to systematically employ the point at infinity (Graustein
1930).
A point lying on the line at infinity is a point at infinity. In particular, a point with trilinear
coordinates 
is a point at infinity if it satisfies
 |
Points at infinity therefore do not have exact trilinear coordinates.
Kimberling centers 
are points at infinity for 
(the Euler infinity
point), 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524,
525, 526, 527, 528, 529, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545,
674, 680, 681, 688, 690, 696, 698, 700, 702, 704, 706, 708, 710, 712, 714, 716, 718,
720, 722, 724, 726, 730, 732, 734, 736, 740, 742, 744, 746, 752, 754, 758, 760, 766,
768, 772, 776, 778, 780, 782, 784, 786, 788, 790, 792, 794, 796, 802, 804, 806, 808,
812, 814, 816, 818, 824, 826, 830, 832, 834, 838, 888, 891, 900, 912, 916, 918, 924,
926, 928, 952, 971, 1154, 1499, 1503, 1510, 1511, 1912, 1938, 1946, 2385, 2386, 2387,
2388, 2389, 2390, 2391, 2392, and 2393 (Weisstein, Oct. 25 and Nov. 20,
2004).
The term point at infinity is also used for complex infinity (Krantz 1999, p. 82).
