Pencil (mathematics)
（重定向自Pencil of planes）
![The Apollonian circles, two orthogonal pencils of circles](/Images/godic/202502/01/Apollonian_circles.svg5943.png")
A pencil in projective geometry is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a projective plane.
More generally, 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