pencilPencil22005-06-22 12:55:472005-06-22 13:09:49Definitionflat pencil\usepackage{amssymb,amscd}
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% define commands hereA \emph{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:
\begin{enumerate}
\item 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 \emph{flat pencil}.
\item 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.
\item A pencil of circles can mean that either these circles all intersect at exactly one point (or share the same tangent line)
\item A pencil of circles can also mean that the circles have two common points of intersection.
\end{enumerate}
\begin{thebibliography}{8}
\bibitem{art} E. Artin, {\em Geometric Algebra}, Wiley-Interscience, Reprint (1988).
\bibitem{cox} H. S. M. Coxeter, {\em Projective Geometry}, Springer-Verlag, 2nd Edition (2003).
\end{thebibliography}