Pencil (mathematics) (nonfiction)

In projective 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 in a projective plane.

In affine geometry with the reflexive variant of parallelism, a set of parallel lines forms an equivalence class called a pencil of parallel lines.[1]

More generally, a pencil is the special case of a linear system of divisors in which the parameter space is a projective line.

A pencil of planes, the family of planes through a given straight line, is sometimes referred to as a fan or a sheaf.