Pencil (mathematics) (nonfiction)
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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 word "pencil" is an English translation of the French phrase ordonnance de lignes ("order of lines"), coined by Girard Desargues.
The original meaning of the English word “pencil” is a fine brush; this is also the meaning of French pinceau (as opposed to French "crayon" = English "pencil"). According to the Oxford English Dictionary the earliest English attestation of "pencil" in its mathematical sense is in a book from as late as 1840. The underlying image is evidently that of lines converging at a single point in the same way that the fine strands on a small pointed brush converge at the tip.
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