The straight line on which all points at infinity lie. The line at infinity is central line 
(Kimberling 1998, p. 150), and has trilinear equation
 |
which follows from the fact that a real triangle will have positive area, and therefore that
 |
The line at infinity passes through Kimberling centers 
for 
(the Euler infinity
point),
511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 674, 680, 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, 1912, 1938, 1946, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393, 2574, 2575, 2771, 2772, 2773, 2774, 2775, 2776, 2777, 2778, 2779, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788, 2789, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799, 2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 2810, 2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 2820, 2821, 2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 2830, 2831, 2832, 2833, 2834, 2835, 2836, 2837, 2838, 2839, 2840, 2841, 2842, 2843, 2844, 2845, 2846, 2847, 2848, 2849, 2850, 2851, 2852, 2853, 2854, 2869, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 2880, 2881, and 2882.
The line at infinity satisfies the remarkable property of being its own complement, and therefore also its own anticomplement.
Instead of the three reflected segments concurring for the isogonal conjugate of a point 
on the circumcircle of a
triangle, they become parallel (and can be considered
to meet at infinity). As 
varies around the circumcircle,
varies through a line called the
line at infinity. Every line is perpendicular to
the line at infinity.
Poncelet was the first to systematically employ the line at infinity (Graustein 1930).
