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A pencil is a set of objects in the context of geometry all of which have some common property.
Pencil of Lines
Let $P$ be a point embedded in a space $S$.
The pencil of lines through $P$ is the set of straight lines $\LL$ in $S$ such that $P$ is on $\LL$.
- Results about pencils can be found here.
- Weisstein, Eric W. "Pencil." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Pencil.html