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In mathematics, a sheaf of planes is the set of all
/ref> It may also be known as a fan of planes or a '' pencil of planes''. When extending the concept of line to the ''
/ref>
In mathematics, a sheaf of planes is the set of all planes
Plane most often refers to:
* Aero- or airplane, a powered, fixed-wing aircraft
* Plane (geometry), a flat, 2-dimensional surface
* Plane (mathematics), generalizations of a geometrical plane
Plane or planes may also refer to:
Biology
* Plane ...
that have the same common line.Definition on ''Mathworld Wolfram''/ref> It may also be known as a fan of planes or a '' pencil of planes''. When extending the concept of line to the ''
line at infinity
In geometry and topology, the line at infinity is a projective line that is added to the affine plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at ...
'', a set of ''parallel planes
In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. '' Parallel curves'' are curves that do not touch each oth ...
'' can be seen as a sheaf
Sheaf may refer to:
* Sheaf (agriculture), a bundle of harvested cereal stems
* Sheaf (mathematics)
In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open s ...
of planes intersecting in a line at infinity. To distinguish it from the more general definition, the adjective ''parallel'' can be added to it, resulting in the expression parallel sheaf of planes.Vitutor: Sheaf of Planes/ref>
See also
*Book embedding
In graph theory, a book embedding is a generalization of planar graph, planar embedding of a Graph (discrete mathematics), graph to embeddings in a ''book'', a collection of half-planes all having the same Line (geometry), line as their boundary ...
, a notion of graph embedding
In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs (homeomorphic images of ,1/math>) ...
onto sheafs of half-plane
In mathematics, the upper half-plane, is the set of points in the Cartesian plane with The lower half-plane is the set of points with instead. Arbitrary oriented half-planes can be obtained via a planar rotation. Half-planes are an example ...
s
Notes