Point at Infinity

A point at infinity, or ideal point, is an idealized limiting point at the end of each line in geometry. In an affine plane, including the Euclidean plane, there is one such ideal point for every pencil of parallel lines, and adjoining all of them produces a projective plane in which no point can any longer be told apart from the others. In the real case a point at infinity closes a line into a topologically closed curve, and adding one to the complex line produces the complex projective line, also called the Riemann sphere, while in hyperbolic space every line instead has two distinct ideal points.