Pencil (mathematics) (nonfiction)

Four lines passing through a given point in a projective plane.

In projective geometry, a pencil 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.

In affine geometry with the reflexive variant of parallelism, a set of parallel lines forms an equivalence class called a pencil of parallel lines.

More generally, a pencil is the special case of a linear system of divisors in which the parameter space is a projective line.

A pencil of planes, the family of planes through a given straight line, is sometimes referred to as a fan or a sheaf.

The term was first used by Girard Desargues (Cremona 1960, p. x).

Fiction cross-reference

• Geometry solvent
• Gnomon algorithm
• Gnomon Chronicles
• Mathematician
• Mathematics

Nonfiction cross-reference

• Girard Desargues (nonfiction)
• Mathematics (nonfiction)

External links:

• Pencil (mathematics) @ Wikipedia
• Pencil @ Wolfram MathWorld