# 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. 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. 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. 3.

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

4. 4.

A pencil of circles can also mean that the circles have two common points of intersection.

## References

• 1 E. Artin, Geometric Algebra, Wiley-Interscience, Reprint (1988).
• 2 H. S. M. Coxeter, , Springer-Verlag, 2nd Edition (2003).
Title pencil Pencil 2013-03-22 15:21:31 2013-03-22 15:21:31 CWoo (3771) CWoo (3771) 5 CWoo (3771) Definition msc 51A99 FanOfLines HyperbolasOrthogonalToEllipses flat pencil