pencil
A pencil is a set of geometric objects, usually either congruent or similar^{} to each other, that share a common incidence property. Below are some of the most commonly encountered pencils:

1.
A pencil of lines usually means a set of straight lines that are incident^{} with one point. If the lines all lie in the same plane, the pencil is sometimes called a flat pencil.

2.
In some cases, a pencil of lines denotes a set of parallel lines^{} in a plane. If a point of infinity^{} is added to the plane, then we are back to the previous example.

3.
A pencil of circles can mean that either these circles all intersect at exactly one point (or share the same tangent line)

4.
A pencil of circles can also mean that the circles have two common points of intersection.
References
 1 E. Artin, Geometric Algebra, WileyInterscience, Reprint (1988).
 2 H. S. M. Coxeter, Projective Geometry^{}, SpringerVerlag, 2nd Edition (2003).
Title  pencil 

Canonical name  Pencil 
Date of creation  20130322 15:21:31 
Last modified on  20130322 15:21:31 
Owner  CWoo (3771) 
Last modified by  CWoo (3771) 
Numerical id  5 
Author  CWoo (3771) 
Entry type  Definition 
Classification  msc 51A99 
Related topic  FanOfLines 
Related topic  HyperbolasOrthogonalToEllipses 
Defines  flat pencil 