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Pencil (mathematics)

Index Pencil (mathematics)

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. [1]

13 relations: Affine geometry, Apollonian circles, Emil Artin, Equivalence class, Geometric Algebra, Lefschetz pencil, Linear system of divisors, Matrix pencil, Pencil (optics), Projective geometry, Projective line, Projective plane, Sheaf of planes.

Affine geometry

In mathematics, affine geometry is what remains of Euclidean geometry when not using (mathematicians often say "when forgetting") the metric notions of distance and angle.

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Apollonian circles

Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa.

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Emil Artin

Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.

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Equivalence class

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.

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Geometric Algebra

Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957.

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Lefschetz pencil

In mathematics, a Lefschetz pencil is a construction in algebraic geometry considered by Solomon Lefschetz, used to analyse the algebraic topology of an algebraic variety V.

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Linear system of divisors

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.

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Matrix pencil

In linear algebra, if A_0, A_1,\dots,A_l are n\times n complex matrices for some nonnegative integer l, and A_l \ne 0 (the zero matrix), then the matrix pencil of degree l is the matrix-valued function defined on the complex numbers L(\lambda).

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Pencil (optics)

In optics, a pencil or pencil of rays is a geometric construct used to describe a beam or portion of a beam of electromagnetic radiation or charged particles, typically in the form of a narrow cone or cylinder.

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Projective geometry

Projective geometry is a topic in mathematics.

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Projective line

In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a point at infinity.

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Projective plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane.

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Sheaf of planes

In mathematics, a sheaf of planes is the set of all planes that have the same common line.

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Redirects here:

Pencil (algebraic geometry), Pencil of curves, Pencil of planes.

References

[1] https://en.wikipedia.org/wiki/Pencil_(mathematics)

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