# Pencil (mathematics)

This article is about a class of geometric objects. For other uses, see Pencil (disambiguation).

A **pencil** in projective geometry 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.

More generally, a **pencil** is the special case of a linear system of divisors in which the parameter space is a projective line. Typical pencils of curves in the projective plane, for example, are written as

- λ
*C*+ μ*C*′ = 0

where

*C*= 0,*C*′ = 0

are plane curves.

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

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## References

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