Pencil (mathematics) (nonfiction): Difference between revisions
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In [[Projective geometry (nonfiction)|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 [[Projective geometry (nonfiction)|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. | In affine geometry with the reflexive variant of parallelism, a set of parallel lines forms an equivalence class called a pencil of parallel lines. | ||
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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 term was first used by [[Girard Desargues (nonfiction)|Girard Desargues]] (Cremona 1960, p. x). | |||
== Fiction cross-reference == | == Fiction cross-reference == | ||
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* [[Geometry solvent]] | * [[Geometry solvent]] | ||
* [[Gnomon algorithm]] | * [[Gnomon algorithm]] | ||
* [[Gnomon Chronicles]] | |||
* [[Mathematician]] | |||
* [[Mathematics]] | * [[Mathematics]] | ||
== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Girard Desargues (nonfiction)]] | |||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
Revision as of 18:54, 9 November 2018
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
Nonfiction cross-reference
External links:
- Pencil (mathematics) @ Wikipedia