Pencil (mathematics)

Pencil (mathematics)

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

: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. [http://www.rism.com/Trig/perspective.htm]

ee also

* Pencil of circles
* Lefschetz pencil
* Matrix pencil


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