Sheaf of planes
In mathematics, a sheaf of planes is the set of all planes that have the same common line.[http://mathworld.wolfram.com/SheafofPlanes.html Definition on Mathworld Wolfram]{{cite journal|last1=Sommerville|first1=D. M. Y.|title=Classification of Geometries with Projective Metric|journal=Proceedings of the Edinburgh Mathematical Society|date=1909|volume=28|pages=25–41|doi=10.1017/S0013091500034763|doi-access=free}} 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, a set of parallel planes can be seen as a sheaf 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.[http://www.vitutor.com/geometry/space/sheaf_planes.html Vitutor: Sheaf of Planes]
See also
- Book embedding, a notion of graph embedding onto sheafs of half-planes