Pencil (mathematics) (nonfiction): Difference between revisions
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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 [[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. | ||
More generally, a pencil is the special case of a linear system of divisors in which the parameter space is a projective line. | 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. | A pencil of planes, the family of planes through a given straight line, is sometimes referred to as a fan or a sheaf. | ||
[[Projective geometry (nonfiction)]] | |||
Revision as of 17:47, 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.