Point at infinity complex field, the set of points at infinity is a manifold. In artistic drawing and technical perspective, the projection on the picture plane of the point at infinity of a class of parallel lines is called their vanishing point. In hyperbolic geometry, points at infinity are typically named ideal points. Unlike Euclidean and elliptic geometries, each line has two points at infinity: given a line "l" and a point "P" not on "l", the right- and left-limiting parallels converge asymptotically to different points at infinity. All points at infinity together form the Cayley absolute or boundary of a hyperbolic plane.
Horizon the distance, stimulated the development of projective geometry which posits a point at infinity where parallel lines meet. In her book "Geometry of an Art" (2007), Kirsti Andersen described the evolution of perspective drawing and science up to 1800, noting that vanishing points need not be on the horizon. In a chapter titled "Horizon", John Stillwell recounted how projective geometry has led to incidence geometry, the modern abstract study of line intersection. Stillwell also ventured into foundations of mathematics in a section titled "What are the Laws of Algebra ?" The "algebra of points", originally given by Karl von Staudt