Pencil (mathematics)
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- This article is about a class of geometric objects. For other uses, see Pencil (disambiguation).
A pencil is a family of geometric objects, such as lines, that have a common property, such as passage through a given line in a given plane.
In more technical language, 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
- λC + μC′ = 0
where
- C = 0, C′ = 0
are plane curves.
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