Pencil (mathematics) (nonfiction): Difference between revisions
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A pencil of planes, the family of planes through a given straight line, is sometimes referred to as a fan or a sheaf. | A pencil of planes, the family of planes through a given straight line, is sometimes referred to as a fan or a sheaf. | ||
The | The word "pencil" is an English translation of the French phrase ''ordonnance de lignes'' ("order of lines"), coined by [[Girard Desargues (nonfiction)|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. | |||
== Fiction cross-reference == | == Fiction cross-reference == | ||
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* [https://en.wikipedia.org/wiki/Pencil_(mathematics) Pencil (mathematics)] @ Wikipedia | * [https://en.wikipedia.org/wiki/Pencil_(mathematics) Pencil (mathematics)] @ Wikipedia | ||
* [http://mathworld.wolfram.com/Pencil.html Pencil] @ Wolfram MathWorld | * [http://mathworld.wolfram.com/Pencil.html Pencil] @ Wolfram MathWorld | ||
* [https://hsm.stackexchange.com/questions/5411/where-was-the-word-pencil-first-used-in-projective-geometry-and-what-is-the Where was the word “pencil” first used in (projective) geometry and what is the reason behind this curious name?] | |||
[[Category:Nonfiction (nonfiction)]] | [[Category:Nonfiction (nonfiction)]] | ||
[[Category:Geometry (nonfiction)]] | [[Category:Geometry (nonfiction)]] | ||
[[Category:Mathematics (nonfiction)]] | [[Category:Mathematics (nonfiction)]] | ||
Revision as of 07:32, 10 November 2018
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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.
Fiction cross-reference
Nonfiction cross-reference
External links: