Pencil (geometry)

In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point or the set of circles that pass through two given points. The special case of a two-dimensional pencil in a plane is sometimes referred to as a flat pencil. The three-dimensional case is also called a bundle.

Although the definition of a pencil is rather vague, the common characteristic is that the pencil is defined by a parameter whose value can be determined from any two of its members. Any geometric object can be used in a pencil. The common ones are lines, planes, circles, conics, spheres, and general curves. Even points can be used: a pencil of points is the set of all points on a given line (a more common term for this set is a range of points).