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.
Critical point (mathematics) parallel to the y-axis" and the "projection parallel to the x-axis", respectively. A point of is critical for formula_5, if the tangent to exists and is parallel to the "y"-axis. In that case, the images by formula_5 of the critical point and of the tangent are the same point of the "x"-axis, called the critical value. Thus a point is critical for formula_5 if its coordinates are solution of the system of equations This implies that this definition is a special case of the general definition of a critical point, which is given below. The definition of a critical point